W can do 25% of a work in 30 days, X can do 1/4 of the work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first ?
- (a) W
- (b) X
- (c) Y
- (d) Z ✓ UPSC's answer
Why the answer is (d)
• Calculate the total days required for W: Since W does 25% (1/4) of the work in 30 days, W takes 30 × 4 = 120 days to complete the whole work.
• Calculate the total days required for X: Since X does 1/4 of the work in 10 days, X takes 10 × 4 = 40 days to complete the whole work.
• Calculate the total days required for Y: Since Y does 40% (2/5) of the work in 40 days, Y takes 40 × (5/2) = 100 days to complete the whole work.
• Calculate the total days required for Z: Since Z does 1/3 of the work in 13 days, Z takes 13 × 3 = 39 days to complete the whole work.
• Compare the total days: W (120 days), X (40 days), Y (100 days), and Z (39 days).
• Z requires the least number of days (39) to complete the work, so Z will finish first.
Why the other options are wrong
- (a) W
- W takes 120 days to complete the work, which is the longest duration among all four individuals.
- (b) X
- X takes 40 days to complete the work, which is one day more than Z's 39 days.
- (c) Y
- Y takes 100 days to complete the work, which is significantly longer than Z's 39 days.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.