An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours. If initially the tank was empty and someone started the two pipes together but left the drainage hole open, how many hours will it take for the tank to be filled? (Assume that the rate of drainage is independent of the amount of oil in the tank.) A. 1.50 B. 2.00 C. 2.50 D. 4.00

GATE 2019 · General Aptitude · Work Time · medium

Answer: The tank fills in 2.50 hours (Option C).

1. Express all rates with denominator 20: 1/5 = 4/20; 1/4 = 5/20; 1/20 = 1/20. Net rate = 4/20 + 5/20 - 1/20 = 8/20 = 2/5 tank/hr.
2. Calculate time to fill the tank: T = 1 / (2/5) = 5/2 = 2.5 hours.
3. Verify: In 2.5 hr: pipes add (4/20 + 5/20) × 2.5 = 9/20 × 2.5 = 1.125 tanks. Drain removes 1/20 × 2.5 = 0.125 tanks. Net = 1.125 - 0.125 = 1.000. Tank is exactly full.