Question

An inlet pipe A fill the tank in 15 hour and an outlet pipe B empty the full tank in 20 hour and third inlet pipe C fill the tank at the rate of 50 litre/hour. If all the pipes are opened together, tank will be fill in 10 hour. Find the capacity of the tank?
A) 500 litres
B) 650 litres
C) 600 litres
D) 700 litres

Answer 1

Answer:

Capacity of the tank = (C) = 600 Liters

Step-by-step explanation:

Let the capacity of the tank = X liters

Pipe A takes 15 hrs to fill the tank.

∴ Rate of tank A per hr = A = X ÷ 15 L / hr .....(1)

Pipe B empties the tank in 20 hrs.

∴ Rate of pipe B = B= X ÷ 20  L/hr  ....(This rate will be subtracted as its outlet pipe)  ....(2)

Rate of pipe C = 50 L/hr    ....(3)

When all pipes opened, tank fills in 10 hr.

∴ Combined rate of filling the tank T = X / 10 L/hr   ....(4)

∴ we can write, total rate of filling the tank

T = A - B + C   ....(B is sbtracted as it is an utlet pipe)

∴ X/10 = X/15 - X/20 + 50

∴ X/10 + X/20 - X/15 = 50

∴ (6X + 3X - 4X) ÷ 60 = 50

∴ 5X = 50 × 60

∴ X = 600 Liters

∴ Capacity of the tank = (C) = 600 liters