A tank of 3600 cu m capacity is being filled with water. The delivery of the pump discharging the tank is 20% more than the delivery of the pump filling the same tank. As a result, twelve minutes more time is needed to fill the tank than to discharge it. Determine the rate of delivery of the pump filling the tank.
Answers
Given :- A tank of 3600 cu m capacity is being filled with water. The delivery of the pump discharging the tank is 20% more than the delivery of the pump filling the same tank. As a result, twelve minutes more time is needed to fill the tank than to discharge it. Determine the rate of delivery of the pump filling the tank. ?
Solution :-
Let us assume that,
- The rate of delivery of the pump filling = x cu / min .
- Time taken by discharging pump = y min.
so,
- The rate of delivery of the pump discharging = 20% more than x = 120% of x = (120 * x)/100 = 1.2x cu/min .
- Time taken by filling pump = 12 more min. = (y+12) min.
then,
→ Rate * Time = Rate * Time
→ x * (y + 12) = 1.2x * y
→ xy + 12x = 1.2xy
→ 1.2xy - xy = 12x
→ 0.2xy = 12x
→ 0.2y = 12
→ y = (12/0.2)
→ y = 60 Min.
therefore,
→ Rate of delivery of the pump discharging = (Capacity / Time taken) = (3600/60) = 60 cu/min.
hence,
→ 1.2x = 60
→ x = 50 cu/min. (Ans.)
∴ The rate of delivery of the pump filling the tank is 50 cu/min.
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