Question

A can do a piece of work in 15 days. When he had worked for 3 days, B joined him and the remaining work was finished by both of them in 8 days. In how many days B alone can finish the whole work?

Answer 1

A can do the piece of work in 15 days.
1 day work of A =1/15
Work done in 3days=
$\frac{1}{15} \times 3 = \frac{1}{5}$
Remain work done by A=
$1 - \frac{1}{5} = \frac{4}{5}$
They finish the work in (8-3)=5 days
Both together work in 1 days=
$\frac{1}{5} \times \frac{4}{5} = \frac{4}{25}$
So,Work done by A in one day=1/15
And work done by B in one day=
$\frac{4}{25} - \frac{1}{15} \\ \frac{12 - 5}{75} = \frac{7}{75}$
Hence,
B can alone do the piece of work in=75/7 days