Question

$\text{A}$ and $\text{B}$ can do a piece of work in $20$ days and $\text{B}$ in ​$15$ days. They work together for $2$ days and then $\text{A}$ goes away. In how many days will $\text{B}$ finish the remaining work?​

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Answer 1

Step 1 : Find the remaining work

Given : A and B can do a piece of work in $20$ days.
B can do a piece of work in $15$ days.
They work together for $2$ days and then A goes away

Amount of work done by A and B in $1$ day $=\frac{1}{20}$

Amount of work done by B in $1$ day $=\frac{1}{15}$

A and B work together for $2$ days .

Work done by them in $2$ days $=2\times \frac{1}{20}=\frac{1}{10}$

Remaining work $=1-\frac{1}{10}=\frac{10-1}{10}=\frac{9}{10}$

Step : 2 Time required by B to finish the remaining work

Time required by B to finish the remaining work $=\frac{\frac{9}{10}}{\frac{1}{15}}$

$=\frac{135}{10}$

$=13\frac{1}{2}\text{days}$

Hence, B can finish the remaining work in $13\frac{1}{2}$ days.