Question

Pipe A can fill a tank in $3$ hours. If pipe B can fill the same tank in $2$ hours, how many minutes will it take both pipes to fill $2/3$ of the tank?

• A. $30$
• B. $48$
• C. $54$
• D. $60$
• E. $72$

Answer 1

The correct option is B $48$

Let $t$ be the time in hours for both pipes to fill $\frac{2}{3}$ of the tank

Add rate of filling of pipe A and pipe B to get the rate of filling of both pipes together

we have,

$\frac{1}{3}+\frac{1}{2}=\frac{\frac{2}{3}}{t}$

$2t+3t=6\left(\frac{2}{3}\right)$

$5t=4$

$t=\frac{4}{5}hrs$

Now, converting in minutes

$t=\frac{4}{5}hrs=\left(\frac{4}{5}\right)\times 60=12\times 4=48minutes$

Therefore, in $48minutes$ both pipes will fill $\frac{2}{3}$ of the tank.