A and B can do a piece of work in 24 days and 48 days, respectively. Working together, they completed the work in 12 days with the help of C. How long (in days) will c take to do five-sixth of the work all by himself?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 40.
Assume total work = LCM of 24 and 48 = 48 units
A’s 1-day work = 48/24 = 2 units
B’s 1-day work = 48/48 = 1 unit
Let C’s 1-day work = c units
So total work = 48 units
⇒ (A + B + C)'s 1-day work = 48/12 = 4 units
2 + 1 + c = 4 ⇒ c = 1 unit/day
Total work = 48 units
5/6 of 48 = (5/6) × 48 = 40 units
C does 1 unit/day ⇒ Time = 40/1 = 40 days