Question

$A$ can do a piece of work in $20$ days and $B$ in $15$ days .They worked together on it for $6$ days and then, $A$ left . In how many days will $B$ finish the remaining work ?

• A. $2\frac{5}{2}$
• B. $3\frac{7}{3}$
• C. $2\frac{6}{5}$
• D. $4\frac{1}{2}$

Answer 1

The correct option is D $4\frac{1}{2}$

Given A can do the work in $20$ days and B can do it $15$ days.

Then work done by A in one day $=\frac{1}{20}$

And, work by B in one day $=\frac{1}{15}$

Then, the work done by A & B in one day $=\frac{1}{20}+\frac{1}{15}=\frac{7}{60}$

A & B done 6 days together then work done in A & B in 6 days $=\frac{7}{60}\times 6=\frac{7}{10}$

Then friction of work left $=1-\frac{7}{10}=\frac{3}{10}$

Then B can do $\frac{3}{10}$ work =$\frac{3}{10}\times \frac{15}{1}=\frac{9}{2}=4\frac{1}{2}$ days.