Correct Answer - Option 5 : None of these
Given:
Tap A can fill a tank in = 6 hours
Tap B can fill a tank in = 2 hours
Tap C can empty a tank in = 3 hours
Calculation:
Let the total capacity of cistern be LCM (6, 2, 3) = 6 litres
Now,
Tank filled by A in 1 hour = 6/6
⇒ 1 litre/hour
Tank filled by B in 1 hour = 6/2
⇒ 3 litre/hour
Tank empty by C in 1 hour = 6/3
⇒ (– 2) litre/hour
Tank filled by A, B & C in (1 + 1 +1) hour = (1 + 3 – 2)
⇒ 2 litre/3 hour
In the first 3 hour tank filled by 2 litre
In next 1 hour by tap A tank filled by 1 litre
⇒ In (3 + 1) = 4 hour tank filled by (2 + 1) = 3 litre
In next 1 hour by tap B tank filled by 3 litre
⇒ In (4 + 1) = 5 hour tank filled by (3 + 3) = 6 litre
⇒ In 5 hour the tank become fill
∴ If all three taps are open alternatively 1 hour but start with A, then the whole tank will fill in 5 hours.