Question

$P$ can complete a work in $12$ days working $8$ hours a day. $Q$ can complete the same work in $8$ days working $10$ hours a day. If both $P$ and $Q$ work together, working $8$ hours a day, in how many days can they complete the work?

• A. $5\frac{5}{11}$
• B. $5\frac{6}{11}$
• C. $6\frac{5}{11}$
• D. $6\frac{6}{11}$

Answer 1

Answer: (A)

$5\frac{5}{11}$

$P$ can complete the work in $(12\times 8)$ hrs. $=96$ hours.
$Q$ can complete the work in $(8\times 10)$ hrs. $=80$ hours.
$\therefore$ $P$'s $1$ hour's work $=\frac{1}{96}$ and $Q$'s $1$ hour's work $=\frac{1}{80}$
$(P+Q)$'s $1$ hour's work $=(\frac{1}{96}+\frac{1}{80})=\frac{11}{480}$.
So, both $P$ and $Q$ will finish the work in $\left(\frac{480}{11}\right)$ hrs.
$\therefore$ number of days of $8$ hours each $=(\frac{480}{11}\times \frac{1}{8})=\frac{60}{11}$ days $=5\frac{5}{11}$ days.