Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a constant rate. If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?
Options:
(A) 26.8
(B) 60.0
(C) 120.0
(D) 127.5
Official Answer Key:
C
Step-by-Step Solution & Explanation
• Let the tank capacity be V litres.
• Filling rate of P = V/10 L/min; filling rate of Q = V/6 L/min; draining rate of R = 34 L/min (constant, independent of V).
• With all three operating together, the tank goes from full (V) to empty (0) in 60 minutes, so the net rate = −V/60 L/min.
• Equation: V/10 + V/6 − 34 = −V/60
• Multiply throughout by 60: 6V + 10V − 2040 = −V
• 16V − 2040 = −V ⟹ 17V = 2040 ⟹ V = 120 litres
• Verification: inflow 12+20=32 L/min; net with R = 32−34 = −2 L/min; over 60 min, net change = −120 L, exactly emptying a full 120 L tank. Confirmed.
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