To do a certain work, Q and R work on alternate days, with Q beginning the work on the first day. Q can finish the work alone in 56 days. If the work gets completed in 37.5 days, then R alone can finish half of the same work in:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 14 days.
Q alone can finish the work in 56 days
Q’s 1 day work = 1/56
In 37.5 days,
Q works for 19 days and R works for 18.5 days
Total work = (19 × 1/56) + (18.5 × 1/R) = 1
19/56 + 18.5/R = 1
18.5/R = 1 – 19/56 = 37/56
R = (18.5 × 56) / 37 = 28 days (for full work)
For half work = 28 ÷ 2 = 14 days