Question
Pipes 'P' and 'Q' can fill a tank in 36 minutes and 72
minutes respectively. A third pipe 'R' can empty it in 1 hour 48 minutes. 'P' and 'R' are turned on together. After 30 minutes, 'Q' is also started. Find how long in total it takes to fill the tank.Solution
ATQ,
Let the capacity of tank be 432 litres (LCM of 36, 72 and 108)
Efficiency of 'P' = 432 ÷ 36 = 12 litres/minute
Efficiency of 'Q' = 432 ÷ 72 = 6 litres/minute
Efficiency of 'R' = 432 ÷ 108 = -4 litres/minute
Filled in 30 minutes = (12 - 4) × 30 = 240 litres
Remaining = 432 - 240 = 192 litres
Time for remaining = 192 ÷ (12 + 6 - 4) = 16 minutes
Total time = 30 + 16 = 46 minutes
Statements: L < E; M = O; E >K ≥ M
Conclusions:
I. L < M
II. K = O
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