A booster pump can be used for filling as well as for emptying a tank The capacity of the tank is 24...........

Quantitative Aptitude ( CCS) Pipes&cistern

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?

50 m³/min

60 m³/min

72 m³ /min

None of these

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Explanation:

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

Time required for filling the tank = 2400x minutesTime required for emptying the tank

= 2400x+10 minutesTime required for filling the tank = 2400x minutesTime required for emptying the tank = 2400x+10 minutes
Pump needs 8 minutes lesser to empty the tank than it needs to fill it

⇒2400x−2400x+10=8

⇒300x−300x+10=1

⇒300(x+10)−300x=x(x+10)

⇒3000=x2+10x

⇒x2+10x−3000=0(x+60)(x−50)=0x = 50 or -60

⇒2400x−2400x+10=8

⇒300x−300x+10=1

⇒300(x+10)−300x=x(x+10)

⇒3000=x2+10x

⇒x2+10x−3000 = 0(x+60)(x−50) = 0x = 50 or -60
Since x can not be negative, x=50
filling capacity of the pump = 50 m³ / min.

Hence, option 1 is the correct answer.