{"id":3407,"date":"2022-12-13T04:34:46","date_gmt":"2022-12-13T04:34:46","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3407"},"modified":"2023-01-31T06:50:47","modified_gmt":"2023-01-31T06:50:47","slug":"ncert-solutions-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-2\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.2"},"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; 13 (Direct and Inverse Proportions)\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; 13 Direct and Inverse Proportions <\/strong>Exercise 13.2 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 13: Direct and Indirect Proportions<\/strong><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-13-direct-and-inverse-proportions-ex-13-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 13.1<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 13.2<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>1. Which of the following are in inverse proportion?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> The number of workers on a job and the time to complete the job.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> The time taken for a journey and the distance travelled in a uniform speed.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii)<\/strong> Area of cultivated land and the crop harvested.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv)<\/strong> The time taken for a fixed journey and the speed of the vehicle.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(v)<\/strong> The population of a country and the area of land per person.<\/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><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> The number of workers and the time to complete the job is in inverse proportion.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">As the number of workers increases; the job will take less time to complete. Hence, they are inversely proportional.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> Time and distance covered in direct proportion.<br \/>\nIn more time, more distance can be travelled. Hence, they are not inversely proportional.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)<\/strong> It is a direct proportion because more are of cultivated land will yield more crops.<br \/>\nMore the\u00a0area\u00a0of land cultivated, more crops will be harvested. Hence, they are not inversely proportional.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv)<\/strong> Time and speed are inverse proportion because if time is less, speed is more.<br \/>\nIf speed is increased, it will take less time to complete the fixed journey. Hence, they are inversely proportional.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(v)<\/strong> It is a inverse proportion. If the population of a country increases, the area of land per person decreases.<br \/>\nIf the population of a country increases, then the area of land per person will be decreased. Hence, they are inversely proportional.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>2. In a Television game show, the prize money of Rs.1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3443\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-2.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"855\" height=\"105\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-2.png 855w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-2-300x37.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-2-768x94.png 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-2-480x59.png 480w\" sizes=\"auto, (max-width: 855px) 100vw, 855px\" \/><br \/>\n<\/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;\">Here number of winners and prize money are in inverse proportion because winners are increasing, prize money is decreasing.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">When the number of winners are 4, each winner will get = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{100000}{4}\" alt=\"\\frac{100000}{4}\" align=\"absmiddle\" \/> = Rs. 25,000<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">When the number of winners are 5, each winner will get = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{100000}{5}\" alt=\"\\frac{100000}{5}\" align=\"absmiddle\" \/> = Rs. 20,000<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">When the number of winners are 8, each winner will get = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{100000}{8}\" alt=\"\\frac{100000}{8}\" align=\"absmiddle\" \/> = Rs. 12,500<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">When the number of winners are 10, each winner will get = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{100000}{10}\" alt=\"\\frac{100000}{10}\" align=\"absmiddle\" \/> = Rs. 10,000<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">When the number of winners are 20, each winner will get = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{100000}{20}\" alt=\"\\frac{100000}{20}\" align=\"absmiddle\" \/> = Rs. 5,000<\/span><\/p>\n<p><span style=\"color: #000000;\">Thus, the complete table is shown below:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><span style=\"color: #000000;\"><strong>Number of winners\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/strong>\u00a0<\/span><\/td>\n<td><span style=\"color: #000000;\">1<\/span><\/td>\n<td><span style=\"color: #000000;\">2<\/span><\/td>\n<td><span style=\"color: #000000;\">4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/td>\n<td><span style=\"color: #000000;\">5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/td>\n<td><span style=\"color: #000000;\">8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/td>\n<td><span style=\"color: #000000;\">10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/td>\n<td><span style=\"color: #000000;\">20\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>Prize for winners<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\">1,00,000<\/span><\/td>\n<td><span style=\"color: #000000;\">50,000<\/span><\/td>\n<td><span style=\"color: #000000;\">25,000<\/span><\/td>\n<td><span style=\"color: #000000;\">20,000<\/span><\/td>\n<td><span style=\"color: #000000;\">12,500<\/span><\/td>\n<td><span style=\"color: #000000;\">10,000<\/span><\/td>\n<td><span style=\"color: #000000;\">5,000<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>3. Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3444\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-3.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"585\" height=\"324\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-3.png 663w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-3-300x166.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-13.2-Q-3-480x266.png 480w\" sizes=\"auto, (max-width: 585px) 100vw, 585px\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) <\/strong>Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) <\/strong>Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) <\/strong>How many spokes would be needed, if the angle between a pair of consecutive spokes is 40 degree ?<\/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;\">Here the number of spokes are increasing and the angle between a pair of consecutive spokes is decreasing. So, it is a inverse proportion and angle at the centre of a circle is 360 degree .<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">When the number of spokes is 8, then angle between a pair of consecutive spokes = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{360}{8}\" alt=\"\\frac{360}{8}\" align=\"absmiddle\" \/> = 45 degree<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">When the number of spokes is 10, then angle between a pair of consecutive spokes= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{360}{10}\" alt=\"\\frac{360}{10}\" align=\"absmiddle\" \/> = 36 degree.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">When the number of spokes is 12, then angle between a pair of consecutive spokes= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{360}{12}\" alt=\"\\frac{360}{12}\" align=\"absmiddle\" \/> = 30 degree.<br \/>\n<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><span style=\"color: #000000;\"><strong>Number of spokes\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\">4<\/span><\/td>\n<td><span style=\"color: #000000;\">6<\/span><\/td>\n<td><span style=\"color: #000000;\">8\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/td>\n<td><span style=\"color: #000000;\">10\u00a0 \u00a0 \u00a0\u00a0<\/span><\/td>\n<td><span style=\"color: #000000;\">12\u00a0 \u00a0 \u00a0\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>Angle between spokes<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\">90\u00b0<\/span><\/td>\n<td><span style=\"color: #000000;\">40\u00b0<\/span><\/td>\n<td><span style=\"color: #000000;\">30\u00b0<\/span><\/td>\n<td><span style=\"color: #000000;\">36\u00b0<\/span><\/td>\n<td><span style=\"color: #000000;\">45\u00b0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> Yes, the number of spokes and the angles formed between a pair of consecutive spokes is in inverse proportion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> When the number of spokes is 15, then angle between a pair of consecutive spokes= 360\/15= 24 degree.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)<\/strong> The number of spokes would be needed = 360\/40 = 9<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>4. If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?<\/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;\">Each child gets = 5 sweets<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">24 children will get 24\u00d75 = 120 sweets.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Total number of sweets = 120<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">If the number of children is reduced by 4, then children left = 24 &#8211; 4 = 20<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Now each child will get sweets = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{120}{20}\" alt=\"\\frac{120}{20}\" align=\"absmiddle\" \/> = 6 sweets<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>5. A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?<\/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;\">Let the number of days be x.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Total number of animals = 20 + 10 = 30<br \/>\n<\/span><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 29.697%;\">\n<tbody>\n<tr>\n<td style=\"width: 16.7272%;\"><span style=\"color: #000000;\"><strong>Animals\u00a0<\/strong><\/span><\/td>\n<td style=\"width: 7.27273%;\"><span style=\"color: #000000;\">20<\/span><\/td>\n<td style=\"width: 5.69697%;\"><span style=\"color: #000000;\">30<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 16.7272%;\"><span style=\"color: #000000;\"><strong>Days<\/strong><\/span><\/td>\n<td style=\"width: 7.27273%;\"><span style=\"color: #000000;\">6<\/span><\/td>\n<td style=\"width: 5.69697%;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">Here the number of animals and the number of days are in inverse proportion.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{20}{30}&amp;space;=&amp;space;\\frac{x}{6}\" alt=\"\\frac{20}{30} = \\frac{x}{6}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">30 \u00d7 x = 20 \u00d7 6<br \/>\n<\/span><\/span><\/p>\n<p><span style=\"color: #000000;\">x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{20\\times&amp;space;6}{30}\" alt=\"\\frac{20\\times 6}{30}\" align=\"absmiddle\" \/>\u00a0 \u00a0<span style=\"font-family: georgia, palatino, serif;\">= 4<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence the food will last for four days.<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>6. A contractor estimates that 3 persons could rewire Jasminder\u2019s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?<\/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;\">Let time taken to complete the job be x.<br \/>\n<\/span><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 29.0897%;\">\n<tbody>\n<tr>\n<td style=\"width: 9.0485%;\"><span style=\"color: #000000;\">Persons<\/span><\/td>\n<td style=\"width: 9.51567%; text-align: center;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"width: 17.4323%; text-align: center;\"><span style=\"color: #000000;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.0485%;\"><span style=\"color: #000000;\">Days<\/span><\/td>\n<td style=\"width: 9.51567%; text-align: center;\"><span style=\"color: #000000;\">4<\/span><\/td>\n<td style=\"width: 17.4323%; text-align: center;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here the number of persons and the number of days are in inverse proportion.<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{4}&amp;space;=&amp;space;\\frac{x}{4}\" alt=\"\\frac{3}{4} = \\frac{x}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3\\times&amp;space;4}{4}\" alt=\"\\frac{3\\times 4}{4}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">x = 3<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, 4 persons will complete the job in 3 days.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>7. A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled? <\/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;\">Let the number of boxes be x.<br \/>\n<\/span><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 45.5758%;\">\n<tbody>\n<tr>\n<td style=\"width: 29.6969%;\"><span style=\"color: #000000;\">No. of bottles in each box<\/span><\/td>\n<td style=\"width: 7.75758%; text-align: center;\"><span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"width: 8.12116%; text-align: center;\"><span style=\"color: #000000;\">20<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 29.6969%;\"><span style=\"color: #000000;\">Boxes<\/span><\/td>\n<td style=\"width: 7.75758%; text-align: center;\"><span style=\"color: #000000;\">25<\/span><\/td>\n<td style=\"width: 8.12116%; text-align: center;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here the number of bottles and the number of boxes are in inverse proportion.<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{12}{20}&amp;space;=&amp;space;\\frac{x}{25}\" alt=\"\\frac{12}{20} = \\frac{x}{25}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">12\u00d725 = 20x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{12\\times&amp;space;25}{20}\" alt=\"\\frac{12\\times 25}{20}\" align=\"absmiddle\" \/>\u00a0 = 15<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence 15 boxes would be filled.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>8. A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?<\/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;\">Let the number of machines required be x.<br \/>\n<\/span><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 27.8788%;\">\n<tbody>\n<tr>\n<td style=\"width: 14.7878%;\"><span style=\"color: #000000;\">Days<\/span><\/td>\n<td style=\"width: 7.27274%; text-align: center;\"><span style=\"color: #000000;\">63<\/span><\/td>\n<td style=\"width: 5.81819%; text-align: center;\"><span style=\"color: #000000;\">54<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 14.7878%;\"><span style=\"color: #000000;\">Machines<\/span><\/td>\n<td style=\"width: 7.27274%; text-align: center;\"><span style=\"color: #000000;\">42<\/span><\/td>\n<td style=\"width: 5.81819%; text-align: center;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here the number of machines and the number of days are in inverse proportion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{63}{54}&amp;space;=&amp;space;\\frac{x}{42}\" alt=\"\\frac{63}{54} = \\frac{x}{42}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">63\u00d742 = 54x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{63\\times&amp;space;42}{54}\" alt=\"\\frac{63\\times 42}{54}\" align=\"absmiddle\" \/> \u00a0<\/span><span style=\"font-family: georgia, palatino, serif;\">49<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence 49 machines would be required.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>9. A car takes 2 hours to reach a destination by travelling at the speed of 60 km\/hr. How long will it take when the car travels at the speed of 80 km\/hr?<\/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;\">Let the number of hours be x.<br \/>\n<\/span><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 33.3314%;\">\n<tbody>\n<tr>\n<td style=\"width: 19.2727%;\"><span style=\"color: #000000;\">Speed (km\/hr)<\/span><\/td>\n<td style=\"width: 6.78784%; text-align: center;\"><span style=\"color: #000000;\">60<\/span><\/td>\n<td style=\"width: 7.27273%; text-align: center;\"><span style=\"color: #000000;\">80<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 19.2727%;\"><span style=\"color: #000000;\">Time (hours)<\/span><\/td>\n<td style=\"width: 6.78784%; text-align: center;\"><span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"width: 7.27273%; text-align: center;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here the speed of car and time are in inverse proportion.<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{60}{80}&amp;space;=&amp;space;\\frac{x}{2}\" alt=\"\\frac{60}{80} = \\frac{x}{2}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">60 \u00d7 2 = 80x<br \/>\nx = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{60\\times&amp;space;2}{80}\" alt=\"\\frac{60\\times 2}{80}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{2}\" alt=\"\\frac{3}{2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/> hrs.<br \/>\nHence the car will take <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?1\\frac{1}{2}\" alt=\"1\\frac{1}{2}\" align=\"absmiddle\" \/> hours to reach its destination.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>10. Two persons could fit new windows in a house in 3 days.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> One of the persons fell ill before the work started. How long would the job take now?<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> How many persons would be needed to fit the windows in one day?<\/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)<\/strong> Let the number of days be x.<br \/>\n<\/span><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 36.9696%;\">\n<tbody>\n<tr>\n<td style=\"width: 15.8721%;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Persons <\/span><\/td>\n<td style=\"width: 3.10559%; text-align: center;\"><span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"width: 3.10559%; text-align: center;\"><span style=\"color: #000000;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 15.8721%;\"><span style=\"color: #000000;\">Days<\/span><\/td>\n<td style=\"width: 3.10559%; text-align: center;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"width: 3.10559%; text-align: center;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here the number of persons and the number of days are in inverse proportion.<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{1}&amp;space;=&amp;space;\\frac{x}{3}\" alt=\"\\frac{2}{1} = \\frac{x}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">6 = x<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Or x = 6 days<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> Let the number of persons be x.<br \/>\n<\/span><\/p>\n<table style=\"border-collapse: collapse; width: 36.9696%;\">\n<tbody>\n<tr>\n<td style=\"width: 15.8721%;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Persons <\/span><\/td>\n<td style=\"width: 3.10559%; text-align: center;\"><span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"width: 3.10559%; text-align: center;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 15.8721%;\"><span style=\"color: #000000;\">Days<\/span><\/td>\n<td style=\"width: 3.10559%; text-align: center;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"width: 3.10559%; text-align: center;\"><span style=\"color: #000000;\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here the number of persons and the number of days are in inverse proportion.<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{x}=\\frac{1}{3}\" alt=\"\\frac{2}{x}=\\frac{1}{3}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">6 = x<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Or x = 6 persons<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>11. A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?<\/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;\">Let the duration of each period be x.<br \/>\n<\/span><\/span><\/p>\n<table style=\"border-collapse: collapse; width: 71.1496%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Period<\/span><\/td>\n<td style=\"width: 19.6364%; text-align: center;\"><span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"width: 16.679%; text-align: center;\"><span style=\"color: #000000;\">9<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Duration of periods (in minutes)<\/span><\/td>\n<td style=\"width: 19.6364%; text-align: center;\"><span style=\"color: #000000;\">45<\/span><\/td>\n<td style=\"width: 16.679%; text-align: center;\"><span style=\"color: #000000;\">x<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here the number of periods and the duration of periods are in inverse proportion.<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{9}&amp;space;=&amp;space;\\frac{x}{45}\" alt=\"\\frac{8}{9} = \\frac{x}{45}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">8 \u00d7 45 = 9x<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">x = 40<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, duration of each period would be 40 minutes.<\/span><\/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: 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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; 13 (Direct and Inverse Proportions)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 13 Direct and Inverse Proportions Exercise 13.2 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 13: Direct and Indirect Proportions NCERT Solution Class [&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":[468,469,445,5],"class_list":["post-3407","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-13-direct-and-inverse-proportions-in-english","tag-ncert-solutions-class-8-maths-chapter-13-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 13 Direct and Inverse Proportions Ex 13.2 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 8 Mathematics\u00a0Chapter - 13 (Direct and Inverse Proportions)\u00a0The NCERT Solutions in 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