Question
Pipe ‘A’ can fill a tank in 16 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. 60, 10 II. 75, 8.5 III. 140, 7Solution
Let the capacity of the tank be ‘80x’ litres. So, efficiency of pipe ‘A’ = 80x ÷ 16 = ‘5x’ litres/hour For: I Efficiency of pipe ‘B’ = 5x × 0.60 = ‘3x’ litres/hour Time taken by both pipes together to fill the tank = 80x ÷ (3x + 5x) = 10 hours Therefore, statement ‘I’ is true. For: II Efficiency of pipe ‘B’ = 5x × 0.75 = 3.75x litres/hour Time taken by both pipes together to fill the tank = 80x ÷ (3.75x + 5x) ~ 9.14 hours Therefore, statement ‘II’ is not true. For: III Efficiency of pipe ‘B’ = 5x × 1.4 = 7x litres/hour Time taken by both pipes together to fill the tank = 80x ÷ (7x + 5x) ~ 6.66 hours Therefore, statement ‘III’ is not true
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