UPSC Prelims 2024 · CSAT
Question 8: Basic Numeracy
X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?
AnswerUPSC’s answer is (c).
X does 1/6 of the work an hour, Y and Z 1/8 each. One person works each hour and nobody works two hours running, so X can work at most hours 1, 3 and 5 of the first six. Best plan: X in odd hours, Y and Z in the even hours, giving 3/6 + 3/8 = 7/8 in six hours. For the last 1/8 let X work in hour 7: (1/8) ÷ (1/6) = 3/4 hour = 45 minutes. Total 6 h 45 min.
Why each option is right or wrong
- (a) Wrong. Six hours at best finish only 7/8 of the work, and the rest needs more than 15 minutes.
- (b) Wrong. The last 1/8 needs at least 45 minutes even with X, the fastest worker.
- (c) Right. 7/8 is done in six hours, then X finishes the last 1/8 in 45 minutes.
- (d) Wrong. 7 hours is what you get if Y or Z must do the last stretch; with X in it, the total is 6 h 45 min.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.