Question
Pipe 'A' can fill a tank in 24 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. 200, 8 II. 50, 16 III. 300, 6Solution
Let the capacity of the tank be '120x' litres.
So, efficiency of pipe 'A' = 120x ÷ 24 = '5x' litres/hour
For: I Efficiency of pipe 'B' = 5x × 2.00 = '10x' litres/hour
Time taken by both pipes together to fill the tank = 120x ÷ (10x + 5x) = 120x ÷ 15x = 8 hours Therefore, statement 'I' is true.
For: II
Efficiency of pipe 'B' = 5x × 0.50 = '2.5x' litres/hour
Time taken by both pipes together to fill the tank = 120x ÷ (2.5x + 5x) = 120x ÷ 7.5x = 16 hours
Therefore, statement 'II' is true.
For: III Efficiency of pipe 'B' = 5x × 3.00 = '15x' litres/hour
Time taken by both pipes together to fill the tank = 120x ÷ (15x + 5x) = 120x ÷ 20x = 6 hours
Therefore, statement 'III' is true.
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