Before we get into the details, let us revisit the definition of ratio and proportion:<\/p>\n\n\n\n
On the other hand, Proportion is a statement that two ratios are similar, i,e. when two ratios are equal then they make a proportion. For instance, if a\/b = c\/d, then a, b, c, and d are in proportion. This can also be represented as a:b :: c:d, where a and d are known as Extremes, while b and c are called Means. It is also worth remembering that the product of mean shall always be equal to the product of extremes, i.e. ad = bc.<\/p>\n\n\n\n
Having understood the definitions, let us look at different types of questions on Ratio and Proportion.<\/p>\n\n\n\n
Given that a:b = 2:3 and b:c = 5:7, compute a:b:c<\/p>\n\n\n\n
Solution:<\/strong> This is one of the easiest types of questions to solve. If you observe, there is a common factor in both the ratios, i.e. \u201cb\u201d, as it is appearing in both the ratios. In the first ratio, the value of b is 3, while in the second it is 5. You can follow the following steps to solve this:<\/p>\n\n\n\n Step 1: Take the LCM of b, i.e. 3 and 5. In this case, it shall be 15 (i.e. 3 x 5, since both are prime numbers).<\/p>\n\n\n\n Step 2: Convert both ratios so that it has the same number, i.e. 15. For instance, in the first ratio, a:b = 2:3, multiply both the numerator and denominator with 5 to get 10:15. In the second ratio, multiply the ratio with 3 to get b:c = 15:21.<\/p>\n\n\n\n Step 3: After the ratios are converted, you will get, a:b = 10:15 and b:c = 15:21. Therefore, a:b:c = 10:15:21, since 15 is common in both ratios.<\/p>\n\n\n\n Hence, your answer will be 10:15:21.<\/p>\n\n\n\n A, B and C entered into a partnership with a profit-sharing ratio of 3:4:5. At the end of the year, their business generated a profit of Rs 24000. How much profit did each of them receive?<\/p>\n\n\n\n Solution:<\/strong> This is also a straightforward question, and will take a few seconds only to solve by following the below-mentioned steps.<\/p>\n\n\n\n Step 1: Sum the total number of parts, i.e. 3+4+5 = 12<\/p>\n\n\n\n Step 2: Calculate the share of each of the partners:<\/p>\n\n\n\n A = 3\/12 x 24000 = 6000<\/p>\n\n\n\n B = 4\/12 x 24000 = 8000<\/p>\n\n\n\n C = 5\/12 x 24000 = 10000<\/p>\n\n\n\n Hence, the answer is A gets 6000, B gets 8000 and C gets 10000<\/p>\n\n\n\n A, B and C entered into a partnership with a profit-sharing ratio such that A will get 2\/9th<\/sup> of B\u2019s share, while C will get 3\/4th<\/sup> of A\u2019s share. At the end of the year, their business generated a profit of Rs 6250. How much profit did each of them receive?<\/p>\n\n\n\n Solution:<\/strong> This is also a straightforward question, and will take a few seconds only to solve by following the below-mentioned steps.<\/p>\n\n\n\n Step 1: Let us first write down the proportion, A:B = 2:9 and C:A = 3:4<\/p>\n\n\n\n Step 2: Take the LCM of A, i.e. 2 and 4. In this case, it shall be 4.<\/p>\n\n\n\n Step 3: Convert both ratios so that it has the same number, i.e. 4. For instance, in the first ratio, A:B = 2:9, multiply both the numerator and denominator with 2 to get 4:18. In the second ratio, multiply the ratio with 1 to get C:A = 3:4.<\/p>\n\n\n\n Step 4: After the ratios are converted, you will get, A:B= 4:18 and C:A = 3:4. Therefore, A:B:C = 4:18:3.<\/p>\n\n\n\n Step 5: Sum the total number of parts, i.e. 4+18+3= 25<\/p>\n\n\n\n Step 6: Calculate the share of each of the partners:<\/p>\n\n\n\n A = 4\/25 x 6250 = 1000<\/p>\n\n\n\n B = 18\/25 x 6250 = 4500<\/p>\n\n\n\n C = 3\/25 x 6250 = 750<\/p>\n\n\n\n Hence, the answer is A gets 1000, B gets 4500 and C gets 750<\/p>\n\n\n\n The sum of the ages of A and B is 59 years. Further, A is 4 years older to C. The ratio of ages of B:C is 4:7. Find the current age of A. Also, calculate A\u2019s age 5 years back.<\/p>\n\n\n\n Solution:<\/strong> You may follow the below-mentioned steps to solve the question.<\/p>\n\n\n\n Step 1: We know A + B = 59. Also, because A is 4 years older than C, the ratio of B:C shall be 55 (i.e. 59 – 4).<\/p>\n\n\n\n Step 2: Since the ratio of B:C is 4:7, hence, solve this to get the age of B and C. For this, sum the total number of parts, i.e. 4+7 = 11, and then equate it with 55. You will get 1 = 5<\/p>\n\n\n\n Step 3: Calculate the age of B and C.<\/p>\n\n\n\n B = 4 x 5 = 20<\/p>\n\n\n\n C = 7 x 5 = 35<\/p>\n\n\n\n Step 4: Now calculate the current age of A:<\/p>\n\n\n\n A + B = 59<\/p>\n\n\n\n A = 59 \u2013 20 = 39<\/p>\n\n\n\n Step 5: Subtract 5 from the current age of A to get A\u2019s age 5 years ago, i.e. 39 \u2013 5 = 34 years<\/p>\n\n\n\n Hence, the current age of A is 39 years, while 5 years back he was 34 years old.<\/p>\n\n\n\n Five years ago, the age of A and B was in the ratio of 6:7. Seven years later, A\u2019s age will 10% less than B\u2019s age. Find the age of B after 10 years.<\/p>\n\n\n\n Solution:<\/strong> In this question, some basic understanding of percentages will also be applied. You may follow the below-mentioned steps to solve the question.<\/p>\n\n\n\n Step 1: Let B\u2019s age after 7 years be X.<\/p>\n\n\n\n Step 2: If B\u2019s age after 7 years is X, then A\u2019s age will be X \u2013 (1\/10)X = (9\/10)X<\/p>\n\n\n\n Step 3: Now that we know the age of A and B, let us put it in the form of a ratio, i.e. A:B = (9\/10)X : X = 9:10<\/p>\n\n\n\n Step 4: Five years ago, the ratio of age of A:B was 6:7, while after five years it is 9:10. The difference between the years is 12 years, i.e.<\/p>\n\n\n\n 3 = 12,<\/p>\n\n\n\n 1 = 4<\/p>\n\n\n\n Step 5: Calculate the age of A and B using the above value:<\/p>\n\n\n\n B\u2019s age after 7 years will be: 10 x 4 = 40 years<\/p>\n\n\n\n B\u2019s age after 10 years will be: 40 + 3 = 43 years<\/p>\n\n\n\n Hence, B\u2019s age after 10 years will be 43 years<\/p>\n\n\n\n We hope this article will be helpful in your preparation and wish you all the best for your exam.<\/p>\n\n\n\n Happy learning!<\/p>\n","protected":false},"excerpt":{"rendered":" Ratio and Proportion is one of the easiest topics. We’ll discuss the important concepts, tips, and tricks to solve questions.<\/p>\n","protected":false},"author":3,"featured_media":33003,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"footnotes":""},"categories":[50,772,16,23],"tags":[1282,227],"class_list":["post-33002","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-lic-aao","category-lic-ado","category-ssc-cgl","category-ssc-chsl","tag-numerical-ability","tag-quantitative-aptitude"],"yoast_head":"\nExample 2:<\/h2>\n\n\n\n
Example 3:<\/h2>\n\n\n\n
Example 4:<\/h2>\n\n\n\n
Example 5:<\/h2>\n\n\n\n