Question

A can do a job in $10$ days and B in $20$ days. They work together but $4$ days before the finish of the job B leaves. Find the total days to finish the job?

• A. $6$
• B. $8$
• C. $12$
• D. $14$

Answer 1

The correct option is B $8$

As A finish the job in $10$ days

Work done by A in $1$ day = $\frac{1}{10}$

Similarly, work done by B in $1$ day = $\frac{1}{20}$

As B leaves 4 days before the completion of work i.e. last 4 days A worked alone.

Let the no. of days A and B worked together be $x$.

$\therefore (\frac{1}{10}+\frac{1}{20})\times x+(\frac{1}{10}\times 4)=1$

$\Rightarrow \frac{3}{20}x+\frac{2}{5}=1$

$\Rightarrow x=4$

$\therefore$total days to finish the job = $\underset{\left(\text{when A and B worked together}\right)}{x}+\underset{\left(\text{when A worked alone}\right)}{4}=4+4=8$