A and B can do a piece of work in 72 days; B and C can do it in 120 days, while A and C can do it in 90 days. In what time can A alone do it?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 120 days
Work with the part of the work done in one day: adding the three pairs counts each person twice, which gives the one-day work of all three together.
One day's work: A + B \(=\displaystyle\frac{1}{72}\), B + C \(=\displaystyle\frac{1}{120}\), A + C \(=\displaystyle\frac{1}{90}\)
Adding: \(2(A+B+C)=\displaystyle\frac{5}{360}+\frac{3}{360}+\frac{4}{360}=\frac{12}{360}=\frac{1}{30}\)
So A + B + C \(=\displaystyle\frac{1}{60}\)
A alone \(=\) (A + B + C) \(-\) (B + C) \(=\displaystyle\frac{1}{60}-\frac{1}{120}=\frac{1}{120}\)
A alone does the work in 120 days