Question

Two inlet pipes P and Q can fill an empty tank in 18 hours and 20 hours respectively. Both the two pipes were opened simultaneously but as soon as the tank was half filled a leak was detected in the bottom of the tank. After closing that leak, the two inlet pipes took 1 hour less to fill the remaining half of the tank than they had taken to fill the first half of the tank. Find how much time the leak would take to empty the filled tank? ​

Answer 1

Solution :-

→ LCM of 18 and 20 = 180 litre = Let capacity of the tank .

so,

→ Efficiency of Pipe P = capacity / Time = 180/18 = 10 litre/hour .

→ Efficiency of Pipe Q = capacity / Time = 180/20 = 9 litre/hour .

then,

→ Time taken by (P + Q) to fill the half tank after leak was closed = 90/(10 + 9) = (90/19) hours.

also given that, they took 1 hour less time to fill the half remaining tank now .

so,

→ With leak they fill first half tank in = (90/19) + 1 = (109/19) hours .

Let us assume that, the capacity of leak is x litre / hour. { Taking water out. }

then,

→ (109/19)[P + Q - x] = 90 litre { first half }

→ (109/19)[10 + 9 - x] = 90

→ 109(19 - x) = 90 * 19

→ 109*19 - 109x = 90*19

→ 109x = 109*19 - 90*19

→ 109x = 19(109 - 90)

→ 109x = 19*19

→ 109x = 361

→ x = (361/109)

therefore,

→ Time taken by the leak to empty the full tank = 180/(361/109) = 180 * (109/361) ≈ 54.35 hours. (Ans.)

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