Question

A can finish a work in 16 days while B can finish the work in 8 days. After A started the work alone, B joined him after 4 days. The total time taken to finish the work is___

Answer 1

A can finish the work in 16 days. In one day he can finish $\left(\frac{100}{16}\right)\%$ of the work.

In 4 days, working alone he will finish $\left[\right(\frac{100}{16})\times 4]=25\%$ of the work.

Now B joins him.

Amount of work left = 100 – 25 = $75\%$

B can do $\left(\frac{100}{8}\right)\%$ of the work.

A and B together can do $\left(\frac{100}{8}\right)\%+\left(\frac{100}{16}\right)\%=\left(\frac{300}{16}\right)\%$ of the work.

Work left $=75\%$ . Hence time taken $=\left[\frac{(75\times 16)}{300}\right]=4$ days.

So, total time taken = 4 + 4 = 8 days.

2nd method:- In 4 days A will finish $25\%$ of work. Remaining work is $75\%$, Efficiency of B is double than A i.e $50\%$ work will done by B and $25\%$ will done by A. Thus it will take 4 days. Total 8 days.