Question

It takes pump (A) $4$ hours to empty a swimming pool. It takes pump (B) $6$ hours to empty the same swimming pool. If the two pumps are started together, at what time will the two pumps have emptied $50$% of the water in the swimming pool?

• A. $1hour12minutes$
• B. $1hour20minutes$
• C. $2hour30minutes$
• D. $3hours$
• E. $5hours$

Answer 1

Answer: (A)

$1hour12minutes$

Work efficiency of pump A in emptying pool = $\frac{1}{4}$ per hour

Work efficiency of pump B in emptying pool = $\frac{1}{6}$ per hour

$\therefore$ work done by A and B together = $\frac{1}{4}+\frac{1}{6}=\frac{10}{24}$per hour

Hence time taken to fill the tank $100$% = $\frac{24}{10}$ hours

$\therefore$ time taken to fill $50$% = $\frac{12\times 50}{5\times 100}$ = $1.2$ hours

Since, $1hour=60minutes$

$\therefore 1.2$ hours= $1.2\times 60=72$ minutes

$72$ minutes = $(60+12)$ minutes = $1hour$ $12minutes$

So, the answer is option A