Question

The capacity of a tank is 2400 m3. A pump can be used both for filling and emptying the tank. The emptying capacity of the pump is 10 m3/minute higher than its filling capacity. And also, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump.
A) 46 cub.m/min
B) 44 cub.m/min
C) 48 cub.m/min
D) 50 cub.m/min

Answer 1

Hii dear here is your answer


option b 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

★$\bold{Option-:D}$✔️✔️✔️