Multiple choice

Passage

Directions: The question contains a statement that is followed by quantities I, II and III. Read the information clearly and answer your question accordingly. The options represent the relations between these three quantities K) > L) < M) = N) ≤ O) ≥ For example: Quantity I = 200 Quantity II = 300 Quantity III = 100 (a) K, L (b) L, M (c) L, K (d) O, L (e) L, N Quantity I < Quantity II > Quantity III So, answer is (c)

P, Q, R and S together can complete a job in 16/3 days. P and Q together can complete the same job in 20/3 days. R and S together can complete the same job in 80/3 days. P and S alone can complete the same job in 10 days and 80 days, respectively. The work is started by P and Q together. They worked for 4 days and left and then, R alone worked for 5 days. Time taken by S to complete the remaining job is Y days. Quantity I: Value of Y. Quantity II: The number of days taken by Love and Kush together to complete the whole work, if Love can complete the same work in 15 days and Kush can complete the same work in (Y + 8) days. Quantity III: The number of days taken by Sandy and Linde together to complete the whole work, if Sandy alone can complete the same job in (Y + 3) days and Linde alone can complete the same job in (Y - 2) days.

  1. e

  2. d

  3. a

  4. b

  5. c
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P+Q+R+S = 3/16, P+Q = 3/20, R+S = 3/80. P=1/10, S=1/80. From P+Q=3/20, Q=3/20-1/10=1/20. From R+S=3/80, R=3/80-1/80=2/80=1/40. Work done by P+Q in 4 days = 4*(1/20) = 1/5. Work done by R in 5 days = 5*(1/40) = 1/8. Remaining work = 1 - 1/5 - 1/8 = 27/40. S completes this in (27/40)/(1/80) = 54 days. Y=54. Quantity I=54. Quantity II: Love=15, Kush=62, together = (15*62)/(77) approx 12. Quantity III: Sandy=57, Linde=52, together = (57*52)/(109) approx 27. I > II > III.

AI explanation

Using the work equivalence method, P's daily work is 1/10 and S's is 1/80, so P and Q's combined rate of 3/20 means Q's daily work is 3/20 minus 1/10, equaling 1/20. The group of P and Q works for 4 days to complete 12/20 of the job, and R's daily rate of 1/16 over 5 days completes another 5/16, leaving 15/80 of the job for S, which takes S exactly 15 days, making Quantity I equal to 15. Quantity II compares Love's 15-day rate with Kush's 23-day rate, giving a combined completion time of 15 times 23 divided by 38, or about 9.08 days. Quantity III compares Sandy's 18-day rate with Linde's 13-day rate, resulting in a combined time of 18 times 13 divided by 31, or about 7.55 days. Quantity I is greater than both Quantity II and Quantity III, which corresponds to option a.

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