Question

To complete a piece of work, A and B take 30 days, B and C take 24 days and C and A take 20 days. They all work for 10 days, and then B and C leave. How many more days will A take to finish the work?

Accepted Answer

D. Rates: $A + B = \frac{1}{30}$, $B + C = \frac{1}{24}$, $C + A = \frac{1}{20}$. $2(A + B + C) = \frac{1}{30} + \frac{1}{24} + \frac{1}{20} = \frac{4 + 5 + 6}{120} = \frac{15}{120} = \frac{1}{8}$. $A + B + C = \frac{1}{16}$. Rate of A alone = $(A + B + C) - (B + C) = \frac{1}{16} - \frac{1}{24} = \frac{3 - 2}{48} = \frac{1}{48}$. In 10 days, A, B, and C together do $10 	imes \frac{1}{16} = \frac{5}{8}$ of the work. Remaining work = $1 - \frac{5}{8} = \frac{3}{8}$. Days needed for A alone = $\frac{3/8}{1/48} = 3 	imes 6 = 18$ days.

Time and Work - Remaining Days for A

Explanation

Practise this under exam conditions