S and M can do a piece of work in 9 days, while M alone can finish it in 12 days. In how many days can S alone finish the work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 36 days.
S + M can do the work in 9 days
M alone can do the work in 12 days
Let total work = LCM of 9 and 12 = 36 units (assume total work is 36 units for simplicity)
(S + M)’s rate = 36/9 = 4 units/day
M’s rate = 36/12 = 3 units/day
S’s rate = (S + M)′s rate − M′s rate = 4 − 3 = 1 unit/day
Time = 36/1 = 36 days