Question
Pipe 'A' can fill a tank in 20 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. 25, 16 II. 100, 10 III. 150, 8Solution
Let the capacity of the tank be '100x' litres.
So, efficiency of pipe 'A' = 100x ÷ 20 = '5x' litres/hour
For: I Efficiency of pipe 'B' = 5x × 0.25 = '1.25x' litres/hour
Time taken by both pipes together to fill the tank = 100x ÷ (1.25x + 5x) = 100x ÷ 6.25x = 16 hours
Therefore, statement 'I' is true.
For: II
Efficiency of pipe 'B' = 5x × 1.00 = '5x' litres/hour
Time taken by both pipes together to fill the tank = 100x ÷ (5x + 5x) = 100x ÷ 10x = 10 hours
Therefore, statement 'II' is true.
For: III
Efficiency of pipe 'B' = 5x × 1.50 = '7.5x' litres/hour
Time taken by both pipes together to fill the tank = 100x ÷ (7.5x + 5x) = 100x ÷ 12.5x = 8 hours
Therefore, statement 'III' is true.
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