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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 the following is correct?

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 the following is correct? Correct Answer Any two out of S1, S2 and S3 are sufficient

Total volume = Flow rate of R × Time taken to empty

Total volume = (Flow rate of P + Flow rate of Q - Flow rate of R) × Time taken to fill if all the taps and drains are open

To use equation 1, two quantities are required

S1 gives flow rate of R = 6 litres per minute

S3 gives time taken to empty = 15 hours 20 minutes

∴ Volume of tank = 6 × (15 × 60 + 20) = 5520 litres                            

To use equation 2,

S1: gives the flow rate of R

S2 gives the total time require to fill if all taps and drains are opened.

∴ Volume = (12 + 10 - 6) × (5 × 60 + 45)

⇒ 16 × 345 = 5520 litres

Let the volume of the tank be V litres

By S3: Flow rate of Pipe R = V/ (15 × 60 + 20) = V/920

Substituting in S2

V = (12 + 10 - V/920) × (5 × 60 + 45)

V/345 = 22 - V/920

V/345 + V/920 = 22

168V/57960 + 63V/57960 = 22

231V/57960 = 22

∴ V = 5520 litres

∴ Any two statements are required to find the capacity of the tank

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