Question

A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3. The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?
A) 50 m^3/min
B) 60 m^3/min
C) 72 m^3/min
D) None of these

Answer 1

Hii dear here is your answer


option a is the correct answer
Hope it's help u

Answer 2

$\underline{\underline{\Huge\mathfrak{Solution-: }}}$

●Let the filling capacity of the pump = x m3 / min.

●Then the emptying capacity of the pump = (x + 10) m3 / min.

$\text{Time required for filling the tank = }\dfrac{2400}{x}\text{ minutes}\\\\ \text{Time required for emptying the tank = }\dfrac{2400}{x+10}\text{ minutes} \:$

◆Pump needs 8 minutes lesser to empty the tank than it needs to fill it

$\Rightarrow \dfrac{2400}{x} - \dfrac{2400}{x+10} = 8\\\\ \Rightarrow \dfrac{300}{x} - \dfrac{300}{x+10} = 1\\\\ \Rightarrow 300(x+10)-300x=x(x+10)\\\\\Rightarrow 3000 = x^2+10x\\\\\Rightarrow x^2 + 10x-3000=0\\\\ (x+60)(x-50)=0\\\\\text{x = 50 or -60}$

Since x can not be negative, x=50

i.e.,filling capacity of the pump = 50 m3 / min.

Answer-: Option -A[50 m^3/min]