JIPMAT 2021 (QA) - A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 m^3. The emptying capacity of the pump is 10 m^3 per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank as to fill it. The filling capacity of the pump is | PYQs + Solutions

JIPMAT 2021

Geometry

Solids

Conceptual

A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 $m^{3}$ . The emptying capacity of the pump is 10 $m^{3}$ per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank as to fill it. The filling capacity of the pump is

m^3

/minute

m^3

/minute

m^3

/minute

m^3

/minute

Correct Option: 2

Let filling capacity =

x

m^3

/minute

\newline

Then emptying capacity =

(x + 10)

m^3

/minute

Given tank volume =

2400

m^3

For filling:

\frac{2400}{x} = t

minutes

\newline

For emptying:

\frac{2400}{x+10} = (t-8)

minutes

Therefore:

\newline

\frac{2400}{x} - \frac{2400}{x+10} = 8

\frac{2400(x+10) - 2400x}{x(x+10)} = 8

\frac{24000}{x(x+10)} = 8

24000 = 8x(x+10)

24000 = 8x^2 + 80x

8x^2 + 80x - 24000 = 0

x^2 + 10x - 3000 = 0

Solving quadratic:

\newline

x = 50

x = -60

(reject negative)

Therefore, filling capacity is 50

m^3

/minute.