Question

Pipe A can fill a tank in 120 hours and pipe B can fill the same tank in 12 hours. Both the pipes are opened to fill the tank and after 3 hours pipe $A$ is closed. In how many hours the pipe B will fill the remaining part of the tank.

Answer 1

Let $1$ is the volume of the tank

so flowrate of pipe $A=\frac{1}{120}\frac{m^3}{hr}$

flowrate of pipe $B=\frac{1}{12}\frac{m^3}{hr}$

The remaining portion of the tank after $3$ hrs

$=1-3[\frac{1}{120}+\frac{1}{12}]$

$=1-[\frac{1}{40}+\frac{1}{4}]=\frac{40-(1+10)}{40}$ $=\frac{29}{40}$

Time taken by pipe $B=\frac{29}{40}\times \frac{1}{\frac{1}{12}}$

$=\frac{29\times 12}{40}=8.7hrs$