Question
Pipe 'A' can fill a tank in 15 hours. Pipe 'B' is ____% as
efficient as pipe 'A'. If both pipes are opened simultaneously, the tank will be completely full in ____hours.The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true: I. 100, 7.5 II. 20, 12.5 III. 66.67, 9Solution
Let the capacity of the tank be '75x' litres.
So, efficiency of pipe 'A' = 75x ÷ 15 = '5x' litres/hour
For: I Efficiency of pipe 'B' = 5x × 1.00 = '5x' litres/hour
Time taken by both pipes together to fill the tank = 75x ÷ (5x + 5x) = 75x ÷ 10x = 7.5 hours
Therefore, statement 'I' is true.
For: II
Efficiency of pipe 'B' = 5x × 0.20 = '1x' litres/hour
Time taken by both pipes together to fill the tank = 75x ÷ (1x + 5x) = 75x ÷ 6x = 12.5 hours Therefore, statement 'II' is true.
For: III Efficiency of pipe 'B' = 5x × 0.6667 = '3.33x' litres/hour
Time taken by both pipes together to fill the tank = 75x ÷ (3.33x + 5x) = 75x ÷ 8.33x = 9 hours
Therefore, statement 'III' is true.
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