A booster pump can be used to fill as to empty the tank. The capacity of the tank is 1200 m3. The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump requires 4 minutes lesser to vacant the tank than it requires to fill it. Calculate the filling capacity of the pump is-

A booster pump can be used to fill as to empty the tank. The capacity of the tank is 1200 m³. The emptying capacity of the tank is 10 m³ per minute higher than its filling capacity and the pump requires 4 minutes lesser to vacant the tank than it requires to fill it. Calculate the filling capacity of the pump is-

সঠিক উত্তর

50 m3/min

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Question: A booster pump can be used to fill as to empty the tank. The capacity of the tank is 1200 m³. The emptying capacity of the tank is 10 m³ per minute higher than its filling capacity and the pump requires 4 minutes lesser to vacant the tank than it requires to fill it. Calculate the filling capacity of the pump is-

Solution:
Let, the filling capacity of the pump = x m³/min

Given that,
Capacity of the tank = 1200 m³
Emptying rate is 10 m³/min more than filling rate
Emptying time is 4 minutes less than filling time

Then,
Filling time = 1200/x minutes
Emptying capacity = x+10 m³/min
Emptying time = 1200/(x + 10)

ATQ,
(1200/x) - {1200/(x + 10)} = 4
(1/x) - {1/(x + 10)} = 1/300
(x + 10 - x)/x(x + 10) = 1/300
x² + 10x - 3000 = 0
(x + 60) (x - 50) = 0

So, possible values is,
x = 50 And x = - 60 [not valid]

So, the filling capacity of the pump is 50 m³/min

সকল অপশন

রেফারেন্স মাত্র

64 m3/min

45 m3/min

50 m3/min সঠিক

None of these

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