A water tank has been fitted with two taps P and Q and a drain pipe R. Taps P and Q fill at the rate of 12 litres per minute and 10 litres per minute respectively.
Consider the following statements S1, S2 and S3:
S1: Pipe R drains out at the rate of 6 litres per minute.
S2: If both the taps and the drain pipe are opened simultaneously, then the tank is filled in 5 hours 45 minutes.
S3: Pipe R drains out (fully) the filled tank in 15 hours 20 minutes.
To know what is the capacity of the tank, which one of the following is correct?
- AS2 is only sufficient
- BS1, S2 and S3 are necessary
- CAny two out of S1, S2 and S3 are sufficient
- DNone of the above
Explanation
Let the drain rate be r and capacity C. S1 fixes r = 6; S2 gives C = 345(22 − r); S3 gives C = 920r. Any two of these determine C uniquely (e.g. S1 + S3 gives C = 5520 litres), so any two statements are sufficient, option (C).