Question

$A$ can do a piece of work in $9$ days and $B$ in $18$ days. They began the work together but $3$ days before the completion of work $A$ leaves. The time taken to complete the work is:

• A. $7$ days
• B. $5$ days
• C. $8$ days
• D. $11$ days

Answer 1

Answer: (C)

$8$ days

Work done by $A$ in 1 day $=\frac{1}{9}$

Work done by $B$ in 1 day $=\frac{1}{18}$

Work done by $B$ in last 3 days $=\frac{1}{18}\times 3=\frac{1}{6}$

Remaining work$=1-\frac{1}{6}=\frac{5}{6}$

Work done by A and B in 1 day $=\frac{1}{9}+\frac{1}{18}=\frac{3}{18}=\frac{1}{6}$

Hence no. of days in which A and B worked together is $=\frac{\frac{5}{6}}{\frac{1}{6}}=5days$

Then total time to complete the work $=3+5=8days$.