Question
Two pipes, P and Q, can fill a tank in 60 minutes and 100
minutes, respectively. A third pipe R can empty it in 1 hour 40 minutes. Initially, pipes P and R are opened. After 30 minutes, pipe Q is also opened. How long will it take to completely fill the tank?Solution
ATQ,
Let the tank's capacity be 300 litres (LCM of 60, 100 and 100)
Efficiency of P = 300 ÷ 60 = 5 litres/minute
Efficiency of Q = 300 ÷ 100 = 3 litres/minute
Efficiency of R = 300 ÷ 100 = -3 litres/minute
Tank filled in 30 minutes = (5 - 3) × 30 = 60 litres
Remaining volume = 300 - 60 = 240 litres
Time to fill remaining = 240 ÷ (5 + 3 - 3) = 240 ÷ 5 = 48 minutes
Total time taken = 30 + 48 = 78 minutes
Statements: L < E; M = O; E >K ≥ M
Conclusions:
I. L < M
II. K = O
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