Question
Pipe 'A' can fill a tank in 12 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. 50, 8 II. 80, 6 III. 125, 5Solution
Let the capacity of the tank be '60x' litres. So, efficiency of pipe 'A' = 60x ÷ 12 = '5x' litres/hour
For: I
Efficiency of pipe 'B' = 5x × 0.50 = '2.5x' litres/hour
Time taken by both pipes together to fill the tank = 60x ÷ (2.5x + 5x) = 60x ÷ 7.5x = 8 hours
Therefore, statement 'I' is true.
For: II
Efficiency of pipe 'B' = 5x × 0.80 = '4x' litres/hour
Time taken by both pipes together to fill the tank = 60x ÷ (4x + 5x) = 60x ÷ 9x ~ 6.67 hours
Therefore, statement 'II' is not true.
For: III
Efficiency of pipe 'B' = 5x × 1.25 = '6.25x' litres/hour
Time taken by both pipes together to fill the tank = 60x ÷ (6.25x + 5x) = 60x ÷ 11.25x ~ 5.33 hours.
Therefore, statement 'III' is not true.
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