Question

$A$ and $B$ can complete a work in $15$ days and $10$ days respectively. They started doing the work together but after $2$ days $B$ had to leave and $A$ alone completed the remaining work. The whole work was completed in:

• A. $8$ days
• B. $10$ days
• C. $12$ days
• D. $15$ days

Answer 1

Answer: (C)

$12$ days

$(A+B)$'s $1$ day's work $(\frac{1}{15}+\frac{1}{10})=\frac{1}{6}$
Work done by $A$ and $B$ in $2$ days $=(\frac{1}{6}\times 2)=\frac{1}{3}$
Remaining work $=(1-\frac{1}{3})=\frac{2}{3}$
Now, $\frac{1}{15}$ work done by $A$ in $1$ day.
$\therefore$ $\frac{2}{3}$ work will be done by $A$ in $(15\times \frac{2}{3})=10$ days.
Hence, the total time taken $=(10+2)=12$ days.