Geometry

Solids

Medium

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

40 $m^3$ /minute

50 $m^3$ /minute

60 $m^3$ /minute

80 $m^3$ /minute

✅ Correct Option: 2

Let filling capacity = $x$ $m^3$ /minute

Then emptying capacity = $(x + 10)$ $m^3$ /minute

Given tank volume = $2400$ $m^3$

For filling: $\frac{2400}{x} = t$ minutes

For emptying: $\frac{2400}{x+10} = (t-8)$ minutes

Therefore:

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

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

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

$24000 = 8x(x+10)$

$24000 = 8x^2 + 80x$

$8x^2 + 80x - 24000 = 0$

$x^2 + 10x - 3000 = 0$

Solving quadratic:

$x = 50$ or $x = -60$ (reject negative)

Therefore, filling capacity is 50 $m^3$ /minute.

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