Two pipes P and Q can fill a tank in 60 minutes and 30 minutes respectively. Third pipe R drains 5 litres of water per minute. If all the three pipes are opened it took 2 hours to fill the tank. What is the capacity of the tank ?
Answer & explanation
Correct answer: option 4
The correct answer is option (4) : 120 litre
Let the 3rd pipe take t min to empty the full tank
According to given,
$\frac{1}{60}+\frac{1}{30}-\frac{1}{t}=\frac{1}{120}$
$\frac{1}{t}=\frac{1}{60}+\frac{1}{30}-\frac{1}{120}$
$\frac{1}{t}=\frac{2+4-1}{120}$
$\frac{1}{t}=\frac{5}{120}$
∴ Volume of water drained by 3rd pipe in 1 min = 5 litre
Volume of water drained by 3rd pipe in 24 min = 5 × 24 litre = 120 litre
Hence the capacity of the tank $=120\, litre $