Question

$A$ and $B$ can together finish a work in $30$ days. They worked together for $20$ days and then $B$ left. After another $20$ days, $A$ finished the remaining work. In how many days $A$ alone can finish the job?

• A. 40
• B. 54
• C. 60
• D. 59

Answer 1

The correct option is C. $60$

Total time taken by $A$ and $B$ to finish a units of work $=30$ days

Therefore work done by $A$ and $B$ in $1$ day $=\frac{1}{30}$ units of total work

Now, total work done in $20$ days $=\frac{1}{30}\times 20=\frac{2}{3}$ units of work

Hence, amount of work left $=1-\frac{2}{3}=\frac{1}{3}$ units of work

This work was completed by $A$ alone in $20$ days.

Therefore, days taken by $A$ to complete a unit of work $=20÷\frac{1}{3}=60$ days

Hence, it would take $60$ days for $A$ to complete the whole work.