{"id":3257,"date":"2022-12-08T11:48:34","date_gmt":"2022-12-08T11:48:34","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3257"},"modified":"2023-01-31T06:53:13","modified_gmt":"2023-01-31T06:53:13","slug":"ncert-solutions-class-8-maths-chapter-8-comparing-quantities-ex-8-3","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-8-comparing-quantities-ex-8-3\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 8 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 8 (Comparing Quantities)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 8 Mathematics <strong>Chapter &#8211; 8 Comparing Quantities <\/strong>Exercise 8.3 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><strong>Chapter 8: Comparing Quantities<\/strong><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-8-comparing-quantities-ex-8-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 8.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-8-comparing-quantities-ex-8-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 8.2<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 8.3\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>1. Calculate the amount and compound interest on<br \/>\n<\/strong><\/span><strong>(a)<\/strong> \u20b9 10,800 for 3 years at <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?12\\frac{1}{2}\" alt=\"12\\frac{1}{2}\" align=\"absmiddle\" \/> % per annum compounded annually<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(b)<\/strong> \u20b9 18,000 for <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{1}{2}\" alt=\"2\\frac{1}{2}\" align=\"absmiddle\" \/> years at 10% per annum compounded annually<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(c)<\/strong> \u20b9 62,500 for <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/> years at 8% per annum compounded half yearly<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(d)<\/strong> \u20b9 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify)<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(e)<\/strong> \u20b9 10,000 for 1 year at 8% per annum compounded half yearly<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><strong>(a) <\/strong>\u20b9 10,800 for 3 years at <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?12\\frac{1}{2}\" alt=\"12\\frac{1}{2}\" align=\"absmiddle\" \/> % per annum compounded annually<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Principal (P) = \u20b9 10,800<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Rate (R) = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?12\\frac{1}{2}\" alt=\"12\\frac{1}{2}\" align=\"absmiddle\" \/>% = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{25}{2}\" alt=\"\\frac{25}{2}\" align=\"absmiddle\" \/> % (annual)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Number of years (n) = 3<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount (A) = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10800 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{25}{2\\times&amp;space;100}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{25}{2\\times 100} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10800 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{25}{200}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{25}{200} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10800 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{25}{200}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{25}{200} \\right )^3\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10800 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{225}{200}&amp;space;\\right&amp;space;)^3\" alt=\"\\left (\\frac{225}{200} \\right )^3\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10800 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{9}{8}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( \\frac{9}{8} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10800 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{8}\\times&amp;space;\\frac{9}{8}\\times&amp;space;\\frac{9}{8}\" alt=\"\\frac{9}{8}\\times \\frac{9}{8}\\times \\frac{9}{8}\" align=\"absmiddle\" \/> \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 15377.34375<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 15377.34 (approximately)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">C.I. = A \u2013 P = \u20b9 (15377.34 \u2013 10800)<br \/>\n= \u20b9 4,577.34<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(b) \u20b9 18000 for <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{1}{2}\" alt=\"2\\frac{1}{2}\" align=\"absmiddle\" \/>\u00a0 years at 10% per annum compounded annually.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Principal (P) = \u20b9 18,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Rate (R) = 10% annual<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Number of years (n) = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{1}{2}\" alt=\"2\\frac{1}{2}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Since &#8216;n&#8217; is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{1}{2}\" alt=\"2\\frac{1}{2}\" align=\"absmiddle\" \/>\u00a0years, amount can be calculated for 2 years and having amount as principal Simple Interest (S.I.) can be calculated for <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> years because C.I. is only annually<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">First, the amount for 2 years has to be calculated<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 18000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{10}{100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{10}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 18000 <\/span><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{1}{10}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{1}{10} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 18000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{10}\\times&amp;space;\\frac{11}{10}\" alt=\"\\frac{11}{10}\\times \\frac{11}{10}\" align=\"absmiddle\" \/> <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= \u20b9 21780 <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">By taking \u20b9 21780 as principal, the S.I. for the next <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> year will be calculated<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">S.I. =\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> x 21780 x <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{10}{100}\" alt=\"\\frac{10}{100}\" align=\"absmiddle\" \/> <\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 1089<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the interest for the first 2 years = \u20b9 (21780 \u2013 18000) = \u20b9 3780<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">And, interest for the next \u00bd year = \u20b9 1089<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Total C.I. = \u20b9 3780 + \u20b9 1089 <\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 4,869<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = P + C.I.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 18000 + \u20b9 4869<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 22,869<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(c) \u20b9 62500 for <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/> years at 8% per annum compounded half yearly.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;\u00a0<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Principal (P) = \u20b9 62,500<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Rate = 8% per annum or 4% per half-year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Number of years = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">There will be 3 half-years in <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/> years <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Amount, A = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 62500<img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{4}{100}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{4}{100} \\right )^3\" width=\"92\" height=\"48\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 62500<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{1}{25}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{1}{25} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 62500<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{26}{25}&amp;space;\\right&amp;space;)^3\" alt=\"\\left (\\frac{26}{25} \\right )^3\" align=\"absmiddle\" \/> \u00a0<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 70304<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">C.I. = A \u2013 P<br \/>\n= \u20b9 70304 \u2013 \u20b9 62500<br \/>\n= \u20b9 7,804<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(d) \u20b9 8000 for 1 year at 9% per annum compound half yearly. <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(You can use the year-by-year calculation using S.I. formula to verify)<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Principal (P) = \u20b9 8000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Rate of interest = 9% per annum or <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{2}\" alt=\"\\frac{9}{2}\" align=\"absmiddle\" \/>% per half-year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Number of years = 1 year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">There will be 2 half-years in 1 year <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 8000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{9}{2\\times&amp;space;100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{9}{2\\times 100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 8000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{209}{200}&amp;space;\\right&amp;space;)^2\" alt=\"\\left (\\frac{209}{200} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 8736.20<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">C.I. = A \u2013 P<br \/>\n= \u20b9 8736.20 \u2013 \u20b9 8000<br \/>\n= \u20b9 736.20<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(e) \u20b9 10000 for 1 year at 8% per annum compounded half yearly.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Principal (P) = \u20b9 10,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Rate = 8% per annum or 4% per half-year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Number of years = 1 year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">There are 2 half-years in 1 year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{4}{100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{4}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{1}{25}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{1}{25} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 10000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{26}{25}&amp;space;\\right&amp;space;)^2\" alt=\"\\left (\\frac{26}{25} \\right )^2\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 10816<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">C.I. = A \u2013 P<br \/>\n= \u20b9 10816 \u2013 \u20b9 10000<br \/>\n= \u20b9 816<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>2. Kamala borrowed \u20b9 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(Hint: Find A for 2 years with interest compounded yearly and then find S.I. on the 2nd year amount for <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{4}{12}}\" alt=\"\\mathbf{\\frac{4}{12}}\" align=\"absmiddle\" \/> years.)<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;\u00a0<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Principal (P) = \u20b9 26,400<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Rate (R) = 15% per annum<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Number of years (n) = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{4}{12}\" alt=\"2\\frac{4}{12}\" align=\"absmiddle\" \/>\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">First, the amount for 2 years has to be calculated<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/> <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 26400<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{15}{100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{15}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 26400<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{3}{20}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{3}{20} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 26400 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{23}{20}&amp;space;\\right&amp;space;)^2\" alt=\"\\left (\\frac{23}{20} \\right )^2\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 34914<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">By taking \u20b9 34,914 as principal, the S.I. for the next <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{12}&amp;space;=&amp;space;\\frac{1}{3}\" alt=\"\\frac{4}{12} = \\frac{1}{3}\" align=\"absmiddle\" \/> years will be calculated<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">S.I. = 34914 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/> x\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{100}\" alt=\"\\frac{15}{100}\" align=\"absmiddle\" \/> = \u20b9 1745.70<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Interest for the first two years = \u20b9 (34914 \u2013 26400) = \u20b9 8,514<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">And interest for the next 1\/3 year = \u20b9 1,745.70<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Total C.I. = \u20b9 (8514 + \u20b9 1745.70) = \u20b9 10,259.70<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount = P + C.I. = \u20b9 26400 + \u20b9 10259.70 = \u20b9 36,659.70<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>3. Fabina borrows \u20b9 12,500 at 12% per annum for 3 years at simple interest, and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest, and by how much?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Interest paid by Fabina = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(P\\times&amp;space;R\\times&amp;space;T)}{100}\" alt=\"\\frac{(P\\times R\\times T)}{100}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{12500\\times&amp;space;12\\times&amp;space;3}{100}\" alt=\"\\frac{12500\\times 12\\times 3}{100}\" align=\"absmiddle\" \/> <\/span><span style=\"font-family: georgia, palatino, serif;\">= 4500<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">Amount paid by Radha at the end of 3 years = A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">A = 12500<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{10}{100}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{10}{100} \\right )^3\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 12500<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{11}{10}&amp;space;\\right&amp;space;)^3\" alt=\"\\left (\\frac{11}{10} \\right )^3\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 16637.50<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">C.I. = A \u2013 P<br \/>\n= \u20b9 16637.50 \u2013 \u20b9 12500<br \/>\n= \u20b9 4,137.50<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The interest paid by Fabina is \u20b9 4,500 and by Radha is \u20b9 4,137.50<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Thus, Fabina pays more interest = <\/span><span style=\"font-family: georgia, palatino, serif;\">\u20b9 4500 \u2212 \u20b9 4137.50 = \u20b9 362.50<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, Fabina will have to pay \u20b9 362.50 more.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>4. I borrowed \u20b9 12000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">P = \u20b9 12000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">R = 6% per annum<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">T = 2 years<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">S.I. = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(P\\times&amp;space;R\\times&amp;space;T)}{100}\" alt=\"\\frac{(P\\times R\\times T)}{100}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{12000&amp;space;\\times&amp;space;6\\times&amp;space;2}{100}\" alt=\"\\frac{12000 \\times 6\\times 2}{100}\" align=\"absmiddle\" \/> <\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 1440<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">To find the compound interest, the amount (A) has to be calculated<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 12000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{6}{100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{6}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 12000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{3}{50}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{3}{50} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 12000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{53}{50}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{53}{50} \\right )^2\" align=\"absmiddle\" \/> <\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 13483.20<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">\u2234 C.I. = A \u2212 P<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 13483.20 \u2212 \u20b9 12000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 1,483.20<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">C.I. \u2212 S.I.<br \/>\n= \u20b9 1,483.20 \u2212 \u20b9 1,440<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 43.20<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore, the extra amount to be paid is \u20b9 43.20.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>5. Vasudevan invested \u20b9 60000 at an interest rate of 12% per annum compounded half yearly. What amount would he get<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong>\u00a0after 6 months?<br \/>\n<strong>(ii)<\/strong>\u00a0after 1 year?<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(i)\u00a0after 6 months?<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">P = \u20b9 60,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Rate = 12% per annum = 6% per half-year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">n = 6 months = 1 half-year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 60000<img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{6}{100}&amp;space;\\right&amp;space;)^1\" alt=\"\\left ( 1+\\frac{6}{100} \\right )^1\" width=\"92\" height=\"48\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 60000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{3}{50}&amp;space;\\right&amp;space;)\" alt=\"\\left ( 1+\\frac{3}{50} \\right )\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 60000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{53}{50}\" alt=\"\\frac{53}{50}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= \u20b9 63600<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) There are 2 half-years in 1 year<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">So, n = 2<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 60000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{6}{100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{6}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 60000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{3}{50}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{3}{50} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 60000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{53}{50}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{53}{50} \\right )^2\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 67416<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>6. Arif took a loan of \u20b9 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{1\\frac{1}{2}}\" alt=\"\\mathbf{1\\frac{1}{2}}\" align=\"absmiddle\" \/> years if the interest is<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> Compounded annually<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> Compounded half yearly<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) Compounded annually<br \/>\n<\/strong>P = \u20b9 80,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">R = 10% per annum<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">n = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/> years<br \/>\nSince \u2018n\u2019 is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/>\u00a0years, the amount can be calculated for 1 year, and having that amount as principal, S.I. can be calculated for the remaining 1\/2 year because C.I. is always calculated annually.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">First, the amount for 1 year has to be calculated<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 80000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{10}{100}&amp;space;\\right&amp;space;)^1\" alt=\"\\left ( 1+\\frac{10}{100} \\right )^1\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 80000 x <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{10}\" alt=\"\\frac{11}{10}\" align=\"absmiddle\" \/> <\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 88000<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">By taking \u20b9 88,000 as principal, the S.I. for the next \u00bd year will be calculated as<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">S.I. = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(P\\times&amp;space;R\\times&amp;space;T)}{100}\" alt=\"\\frac{(P\\times R\\times T)}{100}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{88000\\times&amp;space;10\\times&amp;space;1}{2\\times&amp;space;100}\" alt=\"\\frac{88000\\times 10\\times 1}{2\\times 100}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= \u20b9 4400<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">Interest for the first year = \u20b9 88000 \u2013 \u20b9 80000 = \u20b9 8000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">And interest for the next \u00bd year = \u20b9 4,400<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Total C.I. = \u20b9 8,000 + \u20b9 4,400 = \u20b9 12,400<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">A = P + C.I.= \u20b9 (80000 + 12400)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 92,400<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) The interest is compounded half yearly<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">Rate = 10% per annum = 5% per half-year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">There will be three half-years in <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/> years<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 80000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{5}{100}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{5}{100} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 80000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{1}{20}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{1}{20} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 80000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{21}{20}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( \\frac{21}{20} \\right )^3\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 92610<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Thus, the difference between the amounts = \u20b9 92,610 \u2013 \u20b9 92,400 = \u20b9 210<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>7. Maria invested \u20b9 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> The amount credited against her name at the end of the second year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> The interest for the 3<sup>rd<\/sup>\u00a0year<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> The amount credited against her name at the end of the second year<br \/>\nP = \u20b9 8,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">R = 5% per annum<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">n = 2 years<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/> <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 8000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{5}{100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{5}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 8000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{21}{20}&amp;space;\\right&amp;space;)^2\" alt=\"\\left (\\frac{21}{20} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= \u20b9 8820<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> The interest for the 3<sup>rd<\/sup>\u00a0year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">P = \u20b9 8,000<br \/>\nR = 5% per annum<br \/>\nT = 1<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">S.I. = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(P\\times&amp;space;R\\times&amp;space;T)}{100}\" alt=\"\\frac{(P\\times R\\times T)}{100}\" align=\"absmiddle\" \/> <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8820&amp;space;\\times&amp;space;5\\times&amp;space;1}{100}\" alt=\"\\frac{8820 \\times 5\\times 1}{100}\" align=\"absmiddle\" \/> <\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 441<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>8. Find the amount and the compound interest on \u20b9 10,000 for <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{1\\frac{1}{2}}\" alt=\"\\mathbf{1\\frac{1}{2}}\" align=\"absmiddle\" \/> years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">P = \u20b9 10,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Rate = 10% per annum = 5% per half-year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">n = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/>\u00a0 years<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">There will 3 half-years in <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/> years<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Amount, A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{5}{100}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{5}{100} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{1}{20}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{1}{20} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 10000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{21}{20}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( \\frac{21}{20} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= \u20b9 11576.25<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Interest earned at 10% p.a. compounded half-yearly = A &#8211; P <\/span><br \/>\n<span style=\"color: #000000;\">= \u20b9 11576.25 &#8211; \u20b9 10000 = \u20b9 1576.25<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Now, let&#8217;s find the interest when compounded annually at the same rate of interest.<br \/>\nHence, for 1 year<br \/>\nR = 10%<br \/>\nn = 1<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">Amount, A = <\/span><span style=\"font-family: georgia, palatino, serif;\">10000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{10}{100}&amp;space;\\right&amp;space;)^1\" alt=\"\\left ( 1+\\frac{10}{100} \\right )^1\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 10000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{11}{10}&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{11}{10} \\right )\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 11000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">By taking \u20b9 11,000 as the principal, the S.I. for the next \u00bd year will be calculated as<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">S.I. = (P x R x T)\/100<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= (11000 x 10 x \u00bd)\/100<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 550<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">So, the interest for the first year = \u20b9 11000 \u2212 \u20b9 10000 = \u20b9 1,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, Total compound interest = \u20b9 1000 + \u20b9 550 = \u20b9 1,550<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">So the difference between two interests = 1576.25 \u2013 1550 = 26.25<br \/>\nTherefore, the interest will be less when compounded annually at the same rate.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>9. Find the amount which Ram will get on \u20b9 4,096, if he gave it for 18 months at <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{12\\frac{1}{2}}\" alt=\"\\mathbf{12\\frac{1}{2}}\" align=\"absmiddle\" \/> per annum, interest being compounded half-yearly.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">P = \u20b9 4,096<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">R = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?12\\frac{1}{2}\" alt=\"12\\frac{1}{2}\" align=\"absmiddle\" \/> per annum = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{25}{2}\" alt=\"\\frac{25}{2}\" align=\"absmiddle\" \/> per annum = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{25}{4}\" alt=\"\\frac{25}{4}\" align=\"absmiddle\" \/> per half-year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">n = 18 months<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">There will be 3 half-years in 18 months<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore, amount A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/> <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 4096 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{25}{4\\times&amp;space;100}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{25}{4\\times 100} \\right )^3\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 4096 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{1}{16}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( 1+\\frac{1}{16} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 4096 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{17}{16}&amp;space;\\right&amp;space;)^3\" alt=\"\\left ( \\frac{17}{16} \\right )^3\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 4913<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore, the required amount is \u20b9 4,913.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>10. The population of a place increased to 54000 in 2003 at a rate of 5% per annum<\/strong><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> find the population in 2001<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> what would be its population in 2005?<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) find the population in 2001<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the population in the year 2001 be &#8216;P&#8217; and the population in 2003 is &#8216;A&#8217; = 54000<br \/>\nR = 5%,<br \/>\nn = 2<br \/>\n<\/span>A = <span style=\"font-family: georgia, palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/> <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">54000 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{5}{100}&amp;space;\\right&amp;space;)^2\" alt=\"P\\left ( 1+\\frac{5}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">54000 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{1}{20}&amp;space;\\right&amp;space;)^2\" alt=\"P\\left ( 1+\\frac{1}{20} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">54000 = P \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{21}{10}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{21}{10} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">P = 54000 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{400}{441}\" alt=\"\\frac{400}{441}\" align=\"absmiddle\" \/> <\/span><br \/>\n<span style=\"color: #000000;\">P = 48979.6 <\/span><br \/>\n<span style=\"color: #000000;\">The population in 2001 = 48980 (approx.)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) Population in the year 2005<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">Now, the population in 2003 is considered as &#8216;P&#8217; = 540000 and the population in 2005 is &#8216;A&#8217;<br \/>\nR = 5%,<br \/>\nn = 2<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">A = <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?P\\left&amp;space;(&amp;space;1+\\frac{R}{100}&amp;space;\\right&amp;space;)^n\" alt=\"P\\left ( 1+\\frac{R}{100} \\right )^n\" width=\"114\" height=\"45\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">A = <\/span><span style=\"font-family: georgia, palatino, serif;\">54000<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(1+\\frac{5}{100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left (1+\\frac{5}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 54000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{21}{20}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{21}{20} \\right )^2\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 59535<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Therefore, the population in the year 2005 would be 59,535.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>11. In a laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">The initial count of bacteria is given as 5,06,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Bacteria at the end of 2 hours = 506000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{2.5}{100}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{2.5}{100} \\right )^2\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 506000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;1+\\frac{1}{40}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( 1+\\frac{1}{40} \\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 506000 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{41}{40}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{41}{40} \\right )^2\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= 531616.25<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Therefore, the count of bacteria at the end of 2 hours will be 5,31,616 (approx.).<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>12. A scooter was bought at \u20b9 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Principal = Cost price of the scooter = \u20b9 42,000<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Depreciation = 8% of \u20b9 42,000 per year<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(P\\times&amp;space;R\\times&amp;space;T)}{100}\" alt=\"\\frac{(P\\times R\\times T)}{100}\" align=\"absmiddle\" \/> <\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{42000\\times&amp;space;8\\times&amp;space;1}{100}\" alt=\"\\frac{42000\\times 8\\times 1}{100}\" align=\"absmiddle\" \/> \u00a0<\/span><span style=\"font-family: georgia, palatino, serif;\">= \u20b9 3360<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Thus, the value after 1 year = \u20b9 42000 \u2212 \u20b9 3360 = \u20b9 38,640.<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 32px;\">\n<td style=\"width: 100%; background-color: #f2e079; text-align: center; height: 32px;\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong>NCERT Class 8<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 8 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Mathematics<\/a>\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-sanskrit-ruchira\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">NCERT Solutions Class 8 Sanskrit<\/span><\/strong><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 8 Mathematics\u00a0 Chapter &#8211; 8 (Comparing Quantities)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 8 Comparing Quantities Exercise 8.3 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 8: Comparing Quantities NCERT Solution Class 8 Maths Ex &#8211; 8.1 NCERT [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[442],"tags":[458,459,445,5],"class_list":["post-3257","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-8-comparing-quantities-in-english","tag-ncert-solutions-class-8-maths-chapter-8-in-english","tag-ncert-solutions-class-8-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions 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