A, B and C can do some work in 40 days. A and C together can do twice as much work as B alone. Find the time taken by B to do the whole work.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 120 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and one-day work adds up when people work together. A and C together do twice B’s work, so the joint work of all three is three times B’s work.
One-day work of A, B and C together \(\displaystyle =\frac{1}{40}\)
(A + C) \(=2\)B, so A + B + C \(=3\)B
B’s one-day work \(\displaystyle =\frac{1}{3}\times\frac{1}{40}=\frac{1}{120}\)
B alone takes 120 days