{"id":2878,"date":"2022-12-01T07:56:05","date_gmt":"2022-12-01T07:56:05","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=2878"},"modified":"2023-01-31T06:47:56","modified_gmt":"2023-01-31T06:47:56","slug":"ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-4","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-4\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.4"},"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; 2 (Linear Equations in One Variable)\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; 2 Linear Equations in One Variable <\/strong>Exercise 2.4 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><span style=\"color: #000000;\"><strong>Chapter 2: Linear Equations in One Variable<\/strong><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 2.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 2.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 2.3<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-5\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 2.5<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-6\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 2.6<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 2.4\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Amina thinks of a number and subtracts 5\/2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the number be x,<br \/>\nAccording to the question,<br \/>\n(x \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{2}\" alt=\"\\frac{5}{2}\" align=\"absmiddle\" \/>) \u00d7 8 = 3x<br \/>\n\u21d2 8x \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{40}{2}\" alt=\"\\frac{40}{2}\" align=\"absmiddle\" \/> = 3x<br \/>\n\u21d2 8x \u2013 3x = 20<br \/>\n\u21d2 5x = 20<br \/>\n\u21d2 x = 4<br \/>\nThus, the number is 4.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. A positive number is 5 times another number. If 21 is added to both numbers, then one of the new numbers becomes twice the other new number. What are the numbers?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the positive number be x.<br \/>\nOther number = 5x<br \/>\nAccording to the question,<br \/>\n5x + 21 = 2(x + 21)<br \/>\n\u21d2 5x + 21 = 2x + 42<br \/>\n\u21d2 5x \u2013 2x = 42 \u2013 21<br \/>\n\u21d2 3x = 21<br \/>\n\u21d2 x = 7<br \/>\nOne number = x = 7<br \/>\nOther number = 5x = 5 \u00d7 7 = 35.<br \/>\nThe two numbers are 7 and 35.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let unit place digit be x.<br \/>\nTen\u2019s place digit = 9 \u2013 x<br \/>\nOriginal number = x + 10(9 \u2013 x)<br \/>\nAfter interchanging the digits, the new number = 10(9 &#8211; x) + x<br \/>\nAccording to the question,<br \/>\n10x + (9-x) + 27 = 10(9-x) + x<br \/>\n\u21d2 10x + 9 \u2013 x + 27 = 90 \u2013 10x + x<br \/>\n\u21d2 9x + 36 = 90 \u2013 9x<br \/>\n\u21d2 9x + 9x = 90 \u2013 36<br \/>\n\u21d2 18x = 54<br \/>\n\u21d2 x = 3<br \/>\nOriginal number = 10x + (9 &#8211; x) = (10\u00d73) + (9 &#8211; 3) = 30 + 6 = 36<br \/>\nThus, the number is 36.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. One of the two digits of a two-digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let unit place digit be x.<br \/>\nTen\u2019s place digit = 3x<br \/>\nOriginal two-digit number = 10x + 3x<br \/>\nAfter interchanging the digits, the new number = 30x + x<br \/>\nAccording to the question,<br \/>\n(30x + x) + (10x + 3x) = 88<br \/>\n\u21d2 31x + 13x = 88<br \/>\n\u21d2 44x = 88<br \/>\n\u21d2 x = 2<br \/>\nHence the required number = 10x + 3x = 13x = 13\u00d72 = 26<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Shobo\u2019s mother\u2019s present age is six times Shobo\u2019s present age. Shobo\u2019s age five years from now will be one-third of his mother\u2019s present age. What are their present ages?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let Shobo\u2019s present age be x years.<br \/>\nShobo\u2019s mother\u2019s age = 6x years.<br \/>\nAfter 5 years Shobo\u2019s age will be (x + 5) years.<br \/>\nAccording to the question,<br \/>\n(x + 5) = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/> \u00d7 6x<br \/>\n\u21d2 x + 5 = 2x<br \/>\n\u21d2 2x \u2013 x = 5<br \/>\n\u21d2 x = 5<br \/>\nPresent age of Shobo = x = 5 years<br \/>\nThe present age of Shobo\u2019s mother = 6x = 30 years.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. There is a narrow rectangular plot reserved for a school in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate \u20b9100 per metre, it will cost the village panchayat \u20b975000 to fence the plot. What are the dimensions of the plot?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the length and breadth of the plot be 11x m and 4x m respectively.<br \/>\nRate of fencing per metre = \u20b9100<br \/>\nTotal cost of fencing = \u20b975000<br \/>\nPerimeter of the plot = 2(l + b) = 2(11x + 4x) = 2 \u00d7 15x = 30x<br \/>\nTotal amount of fencing = (30x \u00d7 100)<br \/>\nAccording to the question,<br \/>\n(30x \u00d7 100) = 75000<br \/>\n\u21d2 3000x = 75000<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{75000}{3000}\" alt=\"\\frac{75000}{3000}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 25<br \/>\nLength of the plot = 11x = 11 \u00d7 25 = 275m<br \/>\nBreadth of the plot = 4 \u00d7 25 = 100m.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>7. Hasan buys two kinds of cloth materials for school uniforms; shirt material that costs him \u20b950 per metre and trouser material that costs him \u20b990 per metre. For every 3 meters of the shirt material, he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit, respectively. His total sale is \u20b936,600. How much trouser material did he buy?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the shirt material bought = 3x m<br \/>\nand trouser material bought = 2x m<br \/>\nSelling price of shirt material per meter = \u20b9 50 + 50 \u00d7(12\/100) = \u20b9 56<\/span><br \/>\n<span style=\"color: #000000;\">Selling price of trouser material per meter = \u20b9 90 + 90 \u00d7 (10\/100) = \u20b9 99<\/span><br \/>\n<span style=\"color: #000000;\">Total amount of sale = \u20b936,600<\/span><br \/>\n<span style=\"color: #000000;\">According to the question,<br \/>\n(2x \u00d7 99) + (3x \u00d7 56) = 36600<br \/>\n\u21d2 198x + 168x = 36600<br \/>\n\u21d2 366x = 36600<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{36600}{366}\" alt=\"\\frac{36600}{366}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 100<br \/>\nTotal trouser material he bought = 2x = 2 \u00d7 100 = 200 m.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>8. Half of a herd of deer is grazing in the field, and three-fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the total number of deer be x.<br \/>\nDeer grazing in the field = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{2}\" alt=\"\\frac{x}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Deer playing nearby = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{2}\" alt=\"\\frac{x}{2}\" align=\"absmiddle\" \/> \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{4}\" alt=\"\\frac{3}{4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3x}{8}\" alt=\"\\frac{3x}{8}\" align=\"absmiddle\" \/><br \/>\nDeer drinking water = 9<br \/>\nAccording to the question,<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{2}\" alt=\"\\frac{x}{2}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3x}{8}\" alt=\"\\frac{3x}{8}\" align=\"absmiddle\" \/> + 9 = x <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4x+3x}{8}\" alt=\"\\frac{4x+3x}{8}\" align=\"absmiddle\" \/> + 9 = x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7x}{8}\" alt=\"\\frac{7x}{8}\" align=\"absmiddle\" \/> + 9 = x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7x}{8}\" alt=\"\\frac{7x}{8}\" align=\"absmiddle\" \/> = 9<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8x-7x}{8}\" alt=\"\\frac{8x-7x}{8}\" align=\"absmiddle\" \/> = 9<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = 9 \u00d7 8<br \/>\n\u21d2 x = 72<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>9. A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the age of granddaughter be x and grandfather be 10x.<br \/>\nAlso, he is 54 years older than her.<br \/>\nAccording to the question, 10x = x + 54<br \/>\n\u21d2 10x \u2013 x = 54<br \/>\n\u21d2 9x = 54<br \/>\n\u21d2 x = 6<br \/>\nAge of grandfather = 10x = 10\u00d76 = 60 years.<br \/>\nAge of granddaughter = x = 6 years.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>10. Aman\u2019s age is three times his son\u2019s age. Ten years ago, he was five times his son\u2019s age. Find their present ages.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the age of Aman\u2019s son be x, then the age of Aman will be 3x.<br \/>\nAccording to the question,<br \/>\n5(x \u2013 10) = 3x \u2013 10<br \/>\n\u21d2 5x \u2013 50 = 3x \u2013 10<br \/>\n\u21d2 5x \u2013 3x = -10 + 50<br \/>\n\u21d2 2x = 40<br \/>\n\u21d2 x = 20<br \/>\nAman\u2019s son age = x = 20 years<br \/>\nAman age = 3x = 3\u00d720 = 60 years<\/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; 2 (Linear Equations in One Variable)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 2 Linear Equations in One Variable Exercise 2.4 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 2: Linear Equations in One Variable [&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":[446,447,445,5],"class_list":["post-2878","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-2-linear-equations-in-one-variable-in-english","tag-ncert-solutions-class-8-maths-chapter-2-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) - 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