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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 SI, 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?
S2 is only sufficient
S1, S2 and S3 are necessary
Any two out of SI, S2 and S3 are sufficient
D. None of the above
P= 12 , Q =10, R= -6
Taking S1 or S2
P + Q – R = 12 + 10 - 6 = 16lt/min
5 hours 45 min = 345 min
Volume of tank = 16*345 = 5520 liters
Now taking S1 and S3
15 hrs. 20 min = 920 min
Volume of tank = 6*920 = 5520 liters
Now taking S2, S3 Let the volume of tank v
v= [10+12 – v/920] *345
v = 22 * 345 – 345 v/920
v + 69v/184 = 22*345
253v/184 = 22*345
V = 22*345*184/253
V = 5520 liters Thus, any two of S1, S2 and S3 are sufficient.
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