Three taps A, B and C can fill a tank in 12 hours, 15 hours and 20 hours respectively. The tank is empty when tap A is opened at 7 a.m.; tap B is opened at 10 a.m. and tap C at 11 a.m. At what time will the tank be completely filled?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2 p.m.
Take the tank as the LCM of 12, 15 and 20, that is 60 units, and add what is filled in each interval of the clock.
Hourly filling: A \(=5\) units, B \(=4\) units, C \(=3\) units
7 a.m. to 10 a.m., A alone: \(3\times5=15\) units
10 a.m. to 11 a.m., A and B: \(5+4=9\) units; total 24 units
From 11 a.m., all three fill \(5+4+3=12\) units an hour; the remaining 36 units take \(\frac{36}{12}=3\) hours
11 a.m. \(+\) 3 hours \(=\) 2 p.m.
The tank is full at 2 p.m.