Question

A man can finish a work in 12 days while B can finish the same work in 15 days. If both work together, then calculate the time taken to complete the work.

• A. 6 days
• B. 6 days
• C. 8 days
• D. 4 days

Answer 1

The correct option is A 6 days

A can finish the work in 12 days.

He can finish $100\%$ of the work in 12 days.

In 1 day he can finish $\left(\frac{100}{12}\right)\%=8.33\%$ of the work.

Similarly B can finish $\left(\frac{100}{15}\right)\%=6.67\%$ of the work in 1 day.

When they both work together, they can finish $(8.33+6.67)\%=15\%$ of the work in 1 day

So, to complete $100\%$ of the work, they will take $\left(\frac{100}{15}\right)e=6\left(\frac{2}{3}\right)$ days. Hence option (a).

2nd method:- Total work (W) = 12A = 15B , $B=\frac{4}{5}A$

n(A+B) = W = 12A or 15B (Here, we take 12A).

$n(A+B)=12A,n(A+\frac{4}{5}A),n=\frac{20}{3}=6\left(\frac{2}{3}\right)$days. Option (a).