Question

L and M together can complete a piece of work in 72 days, M and N together can complete it in 120 days, and L and N together in 90 days. In what time can L alone complete the work?

Accepted Answer

D. Let the daily work rate of L, M, and N be $l, m,$ and $n$ respectively. $$l + m = \frac{1}{72}$$ $$m + n = \frac{1}{120}$$ $$l + n = \frac{1}{90}$$ Adding all three equations: $$2(l + m + n) = \frac{1}{72} + \frac{1}{120} + \frac{1}{90} = \frac{5 + 3 + 4}{360} = \frac{12}{360} = \frac{1}{30}$$ $$l + m + n = \frac{1}{60}$$ Subtracting $(m + n)$ from $(l + m + n)$: $$l = \frac{1}{60} - \frac{1}{120} = \frac{1}{120}$$ So, L alone can complete the work in 120 days.

Time taken by L alone

Explanation

Practise this under exam conditions