Question
Pipe 'X' can fill a tank in 24
hours. Pipe 'Y' can fill the same tank in 36 hours. If pipe 'X' is started ___ hours after pipe 'Y', then the tank will be completely full in __ hours after pipe 'X' was first opened. 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. 8, 11.2 II. 11, 10 III. 15, 8.4Solution
ATQ, Let the capacity of the tank be 72 litres. So, efficiency of pipe 'X' = (72/24) = 3 litres/hour And efficiency of pipe 'Y' = (72/36) = 2 litres/hour For I: Tank filled by pipe 'Y' in 8 hours = 2 X 8 = 16 litres And remaining capacity of the tank = 72 - 16 = 56 litres So, time taken by both pipes to fill the tank = 56 ÷ (3 + 2) = 11.2 hours So, statement I is true. For II: Tank filled by pipe 'Y' in 11 hours = 2 X 11 = 22 litres And remaining capacity of the tank = 72 - 22 = 50 litres So, time taken by both pipes to fill the tank = 50 ÷ (3 + 2) = 10 hours So, statement II is true. For III: Tank filled by pipe 'Y' in 15 hours = 2 X 15 = 30 litres And remaining capacity of the tank = 72 - 30 = 42 litres So, time taken by both pipes to fill the tank = 42 ÷ (3 + 2) = 8.4 hours So, statement III is true.
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