Question

An inlet pipe P can fill a giant tank in 15 hours and an outlet pipe Q can empty the full tank in 20 hours.
Pipe R, a third inlet pipe, can fill the tank at the rate of 50 L/Hr. The tank would be full in 10 hours if all the
pipes are opened together. What is the capacity of the tank?​

Answer 1

Given :- An inlet pipe P can fill a giant tank in 15 hours and an outlet pipe Q can empty the full tank in 20 hours. Pipe R, a third inlet pipe, can fill the tank at the rate of 50 L/Hr. The tank would be full in 10 hours if all the pipes are opened together.

To Find :- What is the capacity of the tank ?

Answer :-

Let us assume that, the capacity of the tank is x Litres .

So,

→ Time taken by Pipe A = 15 hours .

then,

→ Rate of tank A = (x/15) L/hr ------ Eqn.(1)

similarly,

→ Rate of pipe B emptying = (x/20) L/hr ---------- Eqn.(2)

also, given that,

→ Rate of pipe C = 50 L/hr --------- Eqn.(3)

and,

→ Rate of all three pipes = (x/10) L/hr .

then,

→ (x/15) - (x/20) + 50 = (x/10)

→ (x/10) + (x/20) - (x/15) = 50

→ (6x + 3x - 4x)/60 = 50

→ (5x/60) = 50

→ (x/60) = 10

→ x = 600 litres (Ans.)

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