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A motor is used to fill and empty the cooler tank. The tank has a capacity of 3360 m3. The emptying capacity of the pump is 20 m3/minute more than its filling capacity and the pump needs 14 minutes lesser to empty the tank than it needs to fill it. What is the filler capacity of the pump?

A motor is used to fill and empty the cooler tank. The tank has a capacity of 3360 m3. The emptying capacity of the pump is 20 m3/minute more than its filling capacity and the pump needs 14 minutes lesser to empty the tank than it needs to fill it. What is the filler capacity of the pump? Correct Answer 60 m<sup style="">3</sup>/minutes

Given:

The capacity of the tank is 3360 m3.

The emptying capacity of the pump is 20 m3/minute more than its filling capacity.

The pump needs 14 minutes lesser to empty the tank than it needs to fill it.

Concept:

Filling capacity never be negative.

Emptying capacity always be negative.

Total capacity is always the difference between fill and emptying capacity.

Formula used:

Work = (time taken/efficiency)

Calculation:

The capacity of the tank = 3360 m3.

Let the filling capacity be x m3/minutes

So time is taken by the pump to filling the tank

⇒ Time = work/efficiency

⇒ Time = (3360/x) minutes

The emptying capacity of the pump is 20 m3/minute more than its filling capacity.

Than the capacity of emptying = (x + 20) m3/minutes

So time is taken by the pump to emptying the tank

⇒ Time = work/efficiency

⇒ Time = minutes

The pump needs 14 minutes lesser to empty the tank than it needs to fill it.

Now we compare the time difference that given in question with the time difference that we get.

⇒ (3360/x) - = 14

⇒ 3360x + 67200 – 3600x = 14x2 + 280x

⇒ x2 + 20x – 4800 = 0

⇒ x2 + 80x – 60x – 4800 = 0

⇒ x(x + 80) – 60(x + 80) = 0

⇒ (x – 60) (x + 80) = 0

⇒ x = 60 or x = -80

We assumed that the filling capacity be x m3/minutes

We know that the filling capacity never be negative.

So we take x = 60

Hence the filing capacity of the pump is 60 m3/minutes.

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