Ratio & Proportion — Set #1 | Practice

{"setId":"b11e2494-fb75-4817-a441-de5a098eb478","setTitle":"Ratio and Proportion – UPSC CSAT","topicName":"Ratio & Proportion","topicSlug":"ratio-proportion","setNumber":1,"totalQuestions":10,"questions":[{"id":"eaadc311-d165-4224-81dc-48f72fc6d2b2","order":1,"statement":"For the 76th Independence Day parade, NCC cadets of 2 colleges SRCC and LSR participated in a ratio of 3:2. The ratio of male and female cadets of college SRCC is 4:1 and that of college LSR is 7:3. If all the male cadets can be divided into a group of 4, 10 and 19 cadets, then find the minimum number of female cadets who participated from both the colleges in the parade.","options":{"A":"240","B":"180","C":"160","D":"120"},"correctOption":"D","solution":"Let total cadets from SRCC and LSR be 30a and 20a. Male cadets from SRCC = (4/5)×30a=24a, female=6a. Male cadets from LSR = (7/10)×20a=14a, female=6a. Total male cadets=24a+14a=38a, which must be divisible by LCM(4,10,19)=380. Minimum value of a=10. Minimum female cadets = 6a+6a=12a=120."},{"id":"2878a72d-c74b-4d80-9c8a-0fd5d4af2b2d","order":2,"statement":"A sum of Rs. 5200 is distributed among P, Q and R in two ratios 1/4:3/2:5/12. What is the difference between the maximum share and the minimum share?","options":{"A":"Rs. 2,300","B":"Rs. 3,500","C":"Rs. 3,000","D":"Rs. 4,500"},"correctOption":"C","solution":"Simplifying the ratio 1/4:3/2:5/12 gives 3:18:5. Let shares be 3n,18n,5n. Given 3n+18n+5n=5200, so 26n=5200, giving n=200. Difference between maximum(18n) and minimum(3n) share = 15n = 15×200 = Rs. 3,000."},{"id":"a5d1a8d9-73df-4971-9d2e-abd27c72de79","order":3,"statement":"A student got twice as many questions wrong as he got right. If he attempted 54 questions in all, how many questions he solved correctly?","options":{"A":"16","B":"18","C":"24","D":"12"},"correctOption":"B","solution":"Let R=right answers, W=wrong answers, with W=2R. Given R+W=54, so R+2R=54, giving 3R=54, so R=18."},{"id":"733a6107-3a2b-4020-9516-0852ba16f30d","order":4,"statement":"'P' and 'Q' together have ₹1,710. If one-fourth of P's share is equal to three-seventh of Q's share, then how much money does 'Q' have?","options":{"A":"710","B":"610","C":"630","D":"690"},"correctOption":"C","solution":"Given (1/4)P=(3/7)Q, so P=(3/7)×(4/1)×Q=(12/7)Q, meaning P:Q=12:7. Q's share=(7/19)×1710=630."},{"id":"b6a8d8e8-37ad-4a30-97da-3a30ca955c49","order":5,"statement":"If the mean proportion of 120 and 'P' is four times the mean proportion of 70 and 18, then the value of 'P' is:","options":{"A":"136","B":"142","C":"174","D":"168"},"correctOption":"D","solution":"Mean proportion of two numbers a,b is √(ab). Given √(120×P)=4×√(70×18). Squaring: 120P=16×70×18, so P=(16×70×18)/120=168."},{"id":"0f2906fb-42e9-4fbf-9933-eafc7c9c1914","order":6,"statement":"The sum of squares of three positive numbers is 2100 and the ratio of the first number to the second number is 2:1 and the ratio of second number to the third number is 2:1. What is the second number?","options":{"A":"40","B":"20","C":"10","D":"50"},"correctOption":"B","solution":"Since a:b=2:1 and b:c=2:1, we get a:b:c=4:2:1. Let a=4x,b=2x,c=x. Given (4x)²+(2x)²+(x)²=2100, so 16x²+4x²+x²=21x²=2100, giving x²=100, x=10. The second number b=2x=20."},{"id":"b0941613-e93b-450c-850a-5efd7559a211","order":7,"statement":"If the ratio of two numbers is 13:17 and their sum is 90, then what is the product of these numbers?","options":{"A":"1800","B":"2210","C":"1669","D":"1989"},"correctOption":"D","solution":"Let the numbers be 13x and 17x. Given 13x+17x=90, so 30x=90, giving x=3. The numbers are 39 and 51. Product = 39×51 = 1989."},{"id":"40b468f5-a94f-4917-9eb4-9330e9ce5c2c","order":8,"statement":"What number must be added to each of these pairs (8, 20) and (24, 48), so that the ratio of the resulting numbers in each pair is same.","options":{"A":"8","B":"6","C":"5","D":"7"},"correctOption":"A","solution":"Let x be added to each number. For the ratios to be equal: (8+x)/(20+x) = (24+x)/(48+x). Cross multiplying and simplifying: 384+56x+x²=480+44x+x², giving 12x=96, so x=8."},{"id":"6d0b22d9-e4c1-4d70-a39c-d58d86f4b238","order":9,"statement":"80 kg of alloy 'A' is mixed with 50 kg of alloy 'B'. If alloy 'A' has Silver and Copper in the ratio 5:3 and alloy 'B' has copper and zinc in the ratio of 1:4, then the quantity (in kg) of Copper in the new alloy is?","options":{"A":"40","B":"30","C":"35","D":"25"},"correctOption":"A","solution":"Copper in 80 kg of alloy A = (3/8)×80=30 kg. Copper in 50 kg of alloy B = (1/5)×50=10 kg. Total copper in new alloy = 30+10=40 kg."},{"id":"176f12a0-a8ea-4173-b6cc-1ec6c63748a9","order":10,"statement":"A sum of money is to be distributed among 'A', 'B', 'C', and 'D' in ratio of 6:5:4:3, respectively. If 'C' gets Rs. 1,000 more than 'D', then what is the share of 'B'?","options":{"A":"Rs. 3,000","B":"Rs. 5,000","C":"Rs. 3,500","D":"Rs. 2,000"},"correctOption":"B","solution":"Let shares be 6x,5x,4x,3x. Given 4x-3x=1000, so x=1000. B's share = 5x=5×1000=Rs. 5,000."}]}