Question

$P$ and $Q$ take $6$ hours and $8$ hours respectively to complete a work. $P$ works for $1$ hour and then $Q$ works for $2$ hours. How much work is done in $3$ hours?

• A. $\frac{5}{12}$
• B. $\frac{12}{7}$
• C. $\frac{12}{5}$
• D. $\frac{7}{12}$

Answer 1

The correct option is A $\frac{5}{12}$

Find work done in an hour, first.
In $1$ Hour $P$ will do $\frac{1}{6}$ part of work
In $1$ Hour $Q$ will do $\frac{1}{8}$ part of work
In $2$ Hour $Q$ will do $\frac{2}{8}=\frac{1}{4}$ part of work

Required work done $=\frac{1}{6}+\frac{1}{4}=\frac{5}{12}$ part of work