Q. A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
(a) 6
(b) 8
(c) 10
(d) 12
Correct Answer: (a) 6
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Person X & Y working together
Let’s say the total work is W. The first person can complete (0.2 * W) = (W/5) of the work in 8 days. So their rate of work is (W/5)/8 = W/40 per day.
The second person can complete (0.25 * W) = (W/4) of the work in 6 days. So their rate of work is (W/4)/6 = W/24 per day.
Working together, their combined rate of work would be (W/40 + W/24) = (3W/120 + 5W/120) = 8W/120 = W/15 per day.
So to complete 40% of the work, or (0.4 * W), it would take them ((0.4 * W)/(W/15)) = 6 days.
