{"id":2874,"date":"2022-12-01T07:55:57","date_gmt":"2022-12-01T07:55:57","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=2874"},"modified":"2023-01-31T06:48:04","modified_gmt":"2023-01-31T06:48:04","slug":"ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-2-linear-equations-in-one-variable-ex-2-2\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.2"},"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 2.2 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-2-3\" 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-2-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 2.4<\/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; 2.2\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. If you subtract \u00bd from a number and multiply the result by <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{2}}\" alt=\"\\mathbf{\\frac{1}{2}}\" align=\"absmiddle\" \/>, you get <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{8}}\" alt=\"\\mathbf{\\frac{1}{8}}\" align=\"absmiddle\" \/>. 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 required number be x.<br \/>\nAccording to the question,<br \/>\n(x \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>) \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{8}\" alt=\"\\frac{1}{8}\" align=\"absmiddle\" \/><\/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\" \/> \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{4}\" alt=\"\\frac{1}{4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{8}\" alt=\"\\frac{1}{8}\" align=\"absmiddle\" \/><\/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{1}{8}\" alt=\"\\frac{1}{8}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{4}\" alt=\"\\frac{1}{4}\" align=\"absmiddle\" \/><\/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{1+2}{8}\" alt=\"\\frac{1+2}{8}\" align=\"absmiddle\" \/><\/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{3}{8}\" alt=\"\\frac{3}{8}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{8}\" alt=\"\\frac{3}{8}\" align=\"absmiddle\" \/> \u00d7 2<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{4}\" alt=\"\\frac{3}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m, more than twice its breadth. What are the length and breadth of the pool?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the breadth of the rectangle swimming pool be = x<br \/>\nThe perimeter of the rectangular swimming pool = 154 m.<br \/>\nAccording to the question,<br \/>\nLength of the rectangle = 2x + 2<br \/>\nPerimeter = 2(length + breadth)<br \/>\n\u21d2 2(2x + 2 + x) = 154 m<br \/>\n\u21d2 2(3x + 2) = 154<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 3x +2 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{154}{2}\" alt=\"\\frac{154}{2}\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 3x = 77 \u2013 2<br \/>\n\u21d2 3x = 75<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{75}{3}\" alt=\"\\frac{75}{3}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 25 m<br \/>\nTherefore, Breadth = x = 25 cm<br \/>\nLength = 2x + 2<br \/>\n= (2 \u00d7 25) + 2<br \/>\n= 50 + 2<br \/>\n= 52 m<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. The base of an isosceles triangle is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{4}{3}}\" alt=\"\\mathbf{\\frac{4}{3}}\" align=\"absmiddle\" \/> cm. The perimeter of the triangle is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{4\\frac{2}{15}}\" alt=\"\\mathbf{4\\frac{2}{15}}\" align=\"absmiddle\" \/>\u00a0cm. What is the length of either of the remaining equal sides?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Let the length of each of equal sides of the triangle be x cm.<br \/>\nBase of isosceles triangle = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{3}\" alt=\"\\frac{4}{3}\" align=\"absmiddle\" \/> cm<br \/>\nPerimeter of triangle = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?4\\frac{2}{15}\" alt=\"4\\frac{2}{15}\" align=\"absmiddle\" \/> cm = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{62}{15}\" alt=\"\\frac{62}{15}\" align=\"absmiddle\" \/><br \/>\nAccording to the question,<br \/>\nPerimeter of the triangle = sum of the three sides<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{3}\" alt=\"\\frac{4}{3}\" align=\"absmiddle\" \/> + x + x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{62}{15}\" alt=\"\\frac{62}{15}\" align=\"absmiddle\" \/> cm <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 2x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{62}{15}\" alt=\"\\frac{62}{15}\" align=\"absmiddle\" \/> &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{3}\" alt=\"\\frac{4}{3}\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 2x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{62-20}{15}\" alt=\"\\frac{62-20}{15}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 2x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{42}{15}\" alt=\"\\frac{42}{15}\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{42}{15}\" alt=\"\\frac{42}{15}\" align=\"absmiddle\" \/> \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{42}{30}\" alt=\"\\frac{42}{30}\" align=\"absmiddle\" \/> cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{5}\" alt=\"\\frac{7}{5}\" align=\"absmiddle\" \/> cm = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{2}{5}\" alt=\"1\\frac{2}{5}\" align=\"absmiddle\" \/> cm<br \/>\nThe length of either of the remaining equal sides is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{2}{5}\" alt=\"1\\frac{2}{5}\" align=\"absmiddle\" \/>\u00a0 cm.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let one number be x<br \/>\nOther number = x + 15<br \/>\nAccording to the question<br \/>\nx + x + 15 = 95<br \/>\n\u21d2 2x + 15 = 95<br \/>\n\u21d2 2x = 95 \u2013 15<br \/>\n\u21d2 2x = 80<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{80}{2}\" alt=\"\\frac{80}{2}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 40<br \/>\nFirst number = x = 40<br \/>\nAnd, other number = x + 15<br \/>\n= 40 + 15 = 55<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Two numbers are in the ratio 5:3. If they differ by 18, 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 two numbers be 5x and 3x.<br \/>\nAccording to the question,<br \/>\n5x \u2013 3x = 18<br \/>\n\u21d2 2x = 18<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{18}{2}\" alt=\"\\frac{18}{2}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 9<br \/>\nThus,<br \/>\nThe numbers are 5x = 5 \u00d7 9 = 45<br \/>\nAnd 3x = 3 \u00d7 9 = 27.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. Three consecutive integers add up to 51. What are these integers?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the three consecutive integers be x, x + 1 and x + 2.<br \/>\nAccording to the question,<br \/>\nx + (x+1) + (x+2) = 51<br \/>\n\u21d2 3x + 3 = 51<br \/>\n\u21d2 3x = 51 \u2013 3<br \/>\n\u21d2 3x = 48<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{48}{3}\" alt=\"\\frac{48}{3}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 16<br \/>\nThus, the required integers are<br \/>\nx = 16,<br \/>\nx + 1 = 17 and<br \/>\nx + 2 = 18<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>7. The sum of three consecutive multiples of 8 is 888. Find the multiples.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the three consecutive multiples of 8 be 8x, 8x + 8 and 8x + 16.<br \/>\nAccording to the question,<br \/>\n8x + (8x + 8) + (8x + 16) = 888<br \/>\n\u21d2 8x + 8x + 8 + 8x + 16 = 888<br \/>\n\u21d2 24x + 24 = 888<br \/>\n\u21d2 24x = 888 \u2013 24<br \/>\n\u21d2 24x = 864<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{864}{24}\" alt=\"\\frac{864}{24}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 36<br \/>\nThus, the required multiples are<br \/>\n8x = 8 \u00d7 36 = 288,<br \/>\n8x + 8 = 8 \u00d7 36 + 8 = 288 + 8 = 296 and<br \/>\n8x + 16 = 8 \u00d7 36 + 16 = 288 + 16 = 304<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>8. Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4, respectively, they add up to 74. Find these numbers.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the three consecutive integers be x, x + 1 and x + 2.<br \/>\nAccording to the question,<br \/>\n2x + 3(x+1) + 4(x+2) = 74<br \/>\n\u21d2 2x + 3x +3 + 4x + 8 = 74<br \/>\n\u21d2 9x + 11 = 74<br \/>\n\u21d2 9x = 74 \u2013 11<br \/>\n\u21d2 9x = 63<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{63}{9}\" alt=\"\\frac{63}{9}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 7<br \/>\nThus, the numbers are:<br \/>\nx = 7,<br \/>\nx + 1 = 8 and<br \/>\nx + 2 = 9<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>9. The ages of Rahul and Haroon are in the ratio 5 : 7. Four years later, the sum of their ages will be 56 years. 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 the ages of Rahul and Haroon be 5x and 7x.<br \/>\nFour years later,<br \/>\nThe ages of Rahul and Haroon will be (5x + 4) and (7x + 4), respectively.<br \/>\nAccording to the question,<br \/>\n(5x + 4) + (7x + 4) = 56<br \/>\n\u21d2 5x + 4 + 7x + 4 = 56<br \/>\n\u21d2 12x + 8 = 56<br \/>\n\u21d2 12x = 56 \u2013 8<br \/>\n\u21d2 12x = 48<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{48}{12}\" alt=\"\\frac{48}{12}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 4<br \/>\nTherefore, Present age of Rahul = 5x = 5 \u00d7 4 = 20<br \/>\nAnd, present age of Haroon = 7x = 7 \u00d7 4 = 28<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>10. The number of boys and girls in a class is in the ratio of 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the number of boys be 7x<br \/>\nand the number of girls be 5x<br \/>\nAccording to the question,<br \/>\n7x = 5x + 8<br \/>\n\u21d2 7x \u2013 5x = 8<br \/>\n\u21d2 2x = 8<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{2}\" alt=\"\\frac{8}{2}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 4<br \/>\nTherefore, number of boys = 7 \u00d7 4 = 28<br \/>\nand, number of girls = 5\u00d74 = 20<br \/>\nTotal number of students = 20 + 28 = 48<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>11. Baichung\u2019s father is 26 years younger than Baichung\u2019s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the age of Baichung be x years.<br \/>\nThe age of his father = x + 29 years,<br \/>\nand the age of his grandfather = x + 29 + 26 = (x + 55) years.<br \/>\nAccording to the question,<br \/>\nx + x + 29 + x + 55 = 135<br \/>\n\u21d2 3x + 84 = 135<br \/>\n\u21d2 3x = 135 \u2013 84<br \/>\n\u21d2 3x = 51<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{51}{3}\" alt=\"\\frac{51}{3}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 17<br \/>\nHence Baichung\u2019s age = 17 years<br \/>\nBaichung\u2019s father\u2019s age = 17 + 29 = 46 years,<br \/>\nand grand father\u2019s age = 46 + 26 = 72 years.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>12. Fifteen years from now, Ravi\u2019s age will be four times his present age. What is Ravi\u2019s present age?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the present age of Ravi be x.<br \/>\nAfter 15 years, his age will be = (x + 15) years<br \/>\nAccording to the question,<br \/>\nx + 15 = 4x<br \/>\n\u21d2 4x \u2013 x = 15<br \/>\n\u21d2 3x = 15<br \/>\n\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{3}\" alt=\"\\frac{15}{3}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 5<br \/>\nTherefore, the present age of Ravi = 5 years.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>13. A rational number is such that when you multiply it by <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{5}{2}}\" alt=\"\\mathbf{\\frac{5}{2}}\" align=\"absmiddle\" \/> and add <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/> to the product, you get <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-7}{12}}\" alt=\"\\mathbf{\\frac{-7}{12}}\" align=\"absmiddle\" \/>. 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 rational be x.<br \/>\nAccording to the question,<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">x \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{2}\" alt=\"\\frac{5}{2}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{7}{12}\" alt=\"-\\frac{7}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5x}{2}\" alt=\"\\frac{5x}{2}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/>\u00a0 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{7}{12}\" alt=\"-\\frac{7}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5x}{2}\" alt=\"\\frac{5x}{2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{7}{12}\" alt=\"-\\frac{7}{12}\" align=\"absmiddle\" \/> \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5x}{2}\" alt=\"\\frac{5x}{2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7-8}{12}\" alt=\"\\frac{-7-8}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5x}{2}\" alt=\"\\frac{5x}{2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-15}{12}\" alt=\"\\frac{-15}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5x}{2}\" alt=\"\\frac{5x}{2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{4}\" alt=\"\\frac{-5}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{4}\" alt=\"\\frac{-5}{4}\" align=\"absmiddle\" \/> \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\" alt=\"\\frac{2}{5}\" align=\"absmiddle\" \/> \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-10}{20}\" alt=\"\\frac{-10}{20}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{1}{2}\" alt=\"-\\frac{1}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Therefore, the rational number is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{1}{2}\" alt=\"-\\frac{1}{2}\" align=\"absmiddle\" \/>.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>14. Lakshmi is a cashier in a bank. She has currency notes of denominations \u20b9100, \u20b950 and \u20b910, respectively. The ratio of the number of these notes is 2 : 3 : 5. The total cash with Lakshmi is \u20b94,00,000. How many notes of each denomination does she have?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the numbers of notes of \u20b9100, \u20b950 and \u20b910 be 2x, 3x and 5x, respectively.<br \/>\nValue of \u20b9100 = 2x \u00d7 100 = 200x<br \/>\nValue of \u20b950 = 3x \u00d7 50 = 150x<br \/>\nValue of \u20b910 = 5x \u00d7 10 = 50x<br \/>\nAccording to the question,<br \/>\n200x + 150x + 50x = 4,00,000<br \/>\n\u21d2 400x = 4,00,000<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4,00,000}{400}\" alt=\"\\frac{4,00,000}{400}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = 1000<br \/>\nNumbers of \u20b9100 notes = 2x = 2000<br \/>\nNumbers of \u20b950 notes = 3x = 3000<br \/>\nNumbers of \u20b910 notes = 5x = 5000<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>15. I have a total of \u20b9300 in coins of denomination \u20b91, \u20b92 and \u20b95. The number of \u20b92 coins is 3 times the number of \u20b95 coins. The total number of coins is 160. How many coins of each denomination are with me?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the number of \u20b9 5 coins be x.<br \/>\nNumber of \u20b9 2 coins = 3x<br \/>\nTotal number of coins = 160<br \/>\nNumber of \u20b9 1 coin = 160 \u2013 (x + 3x) = 160 \u2013 4x<br \/>\nNow,<br \/>\nValue of \u20b95 coins = x \u00d7 5 = 5x<br \/>\nValue of \u20b92 coins = 3x \u00d7 2 = 6x<br \/>\nValue of \u20b91 coins = (160 \u2013 4x) \u00d7 1 = (160 \u2013 4x)<br \/>\nAccording to the question,<br \/>\n5x + 6x + (160 \u2013 4x) = 300<br \/>\n\u21d2 11x + 160 \u2013 4x = 300<br \/>\n\u21d2 7x = 140 <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{140}{7}\" alt=\"\\frac{140}{7}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 20<br \/>\nNumber of \u20b95 coins = x = 20<br \/>\nNumber of \u20b92 coins = 3x = 60<br \/>\nNumber of \u20b91 coins = (160 \u2013 4x) = 160 \u2013 80 = 80<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>16. The organisers of an essay competition decide that a winner in the competition gets a prize of \u20b9100 and a participant who does not win gets a prize of \u20b925. The total prize money distributed is \u20b93,000. Find the number of winners, if the total number of participants is 63.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let the number of winners = x<br \/>\nNumber of participants who does not win the prize = (63 \u2013 x)<br \/>\nAmount got by winners = \u20b9 100 \u00d7 x = \u20b9 100x<br \/>\nAmount got by loosers = \u20b9 (63 \u2013 x) \u00d7 25 = \u20b9 (1575 \u2013 25x)<br \/>\nAccording to the question,<br \/>\n100x + 1575 \u2013 25x = 3000<br \/>\n\u21d2 75x + 1575 = 3000<br \/>\n\u21d2 75x = 3000 \u2013 1575<br \/>\n\u21d2 75x = 1425 <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1425}{75}\" alt=\"\\frac{1425}{75}\" align=\"absmiddle\" \/><br \/>\n\u21d2 x = 19<br \/>\nTherefore, the numbers of winners are 19.<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"width: 100%; 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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 2.2 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-2874","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) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.2 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 8 Mathematics\u00a0Chapter - 2 (Linear Equations in One Variable)\u00a0The NCERT Solutions in 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