Question

Two pipes $A$ and $B$ can fill a cistern in $37\frac{1}{2}$ minutes and 45 minutes respectively. Both the pipes are opened. The cistern will be filled in just half an hour, if pipe $B$ is turned off after $x$ minutes. What is the value of $m\frac{5}{47}$ days, what is the value of m ?

Answer 1

GIven:

Pipe A can fill the cistern in $37\frac{1}{2}$ minutes =$\frac{75}{2}$minutes.

Pipe B can fill the cistern in $45$ minutes.

The L.C.M of $\left(\frac{75}{2}\right)$ and $45$ = $225$

Efficiency of Pipe A =$\frac{225\times 2}{75}=6$ ......Eq:01

Efficiency of Pipe B =$\frac{225}{45}=5$ ......Eq:02

According to questiion:

(Effficiency of A+ Efficiency of B)x +(Efficieny of A) $(30-x)$ =225

$(6+5)x+6(30-x)=225$

$11x+180-6x=225$

$5x=225-180$

$5x=45$

$x=9$

The required value of x is $\text{9}$ minutes.