Two pipes P and Q can and#64257;ll an empty tank in 25 hours and 20 hours respectively. Pipe R alone can empty the completely and#64257;lled 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 and#64257;ll the tank?a)12b)10c)14d)13Correct answer is option 'A'. Can you explain this answer?

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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?

a)
12
b)
10
c)
14
d)
13

Correct answer is option 'A'. Can you explain this answer?

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Two pipes P and Q can ﬁll an empty tank in 25 hours and 20 hour...

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

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