A and B can do a piece of work in 18 days, B and C can do the same work in 32 days and A and C can do the same in 52 days. The time taken by A, B and C together to do the work is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 18 days.
Given: A + B = 1/18
B + C = 1/32
A + C = 1/52
Add all three: (A + B) + (B + C) + (A + C) = 1/18 + 1/32 + 1/52
→ 2(A + B + C) = LCM of 18, 32, 52 = 7488
→ Sum = (416 + 234 + 144) / 7488 = 794 / 7488
Now: A + B + C = (794 / 7488) ÷ 2 = 397 / 7488
Time = 7488 / 397 ≈ 18 days