Two pipes P and Q can ﬁll an empty tank in 25 hours and 20 hours respectively. Pipe R alone can empty the completely ﬁlled tank in 50 hours… — Answer & Discussion

Two pipes P and Q can ﬁll an empty tank in 25 hours and 20 hours respectively. Pipe R alone can empty the completely ﬁlled tank in 50 hours. Firstly both the pipes P and Q are opened and after 8 hours pipe R is also opened. What will be the total time (in hours) taken to completely ﬁll the tank?

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Discussion 1

CCommunity10 May 2019

Time taken by pipe P to fill the tank = 25 hours

Time taken by pipe Q to fill the tank = 20 hours

Time taken by pipe R to empty the tank = 50 hours

Total capacity of tank = Lcm of (25, 20 and 50) = 100 units

Efficiency of pipe P = 100/25 = 4 units/hour

Efficiency of pipe Q = 100/20 = 5 units/hour

Efficiency of pipe Q = – 100/50 = – 2 units/hour

Efficiency of pipe P and Q together = 5 + 4 = 9 units/hour

Efficiency of pipe P, Q and R together = 5 + 4 – 2 = 7 units/hour

Tank filled in 8 hours = 9 × 8 = 72 units

Remaining capacity = 100 – 72 = 28 units

Time taken to fill remaining 28 units = 28/7 = 4 hours

∴ Total time taken to fill the tank = 8 + 4 = 12 hours