Question
A set (Set βPβ) of 4 pipes can fill ______% of a
tank in 5 minutes while another of set (Set βQβ) of 5 pipes can empty the 60% of completely filled tank in 20 minutes. The time taken to fill ________% of tank when the all the pipes of both sets are opened is 4 minutes. 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. 80, 52 II. 64, 38.2 III. 75, 48Solution
For I: For pipes of Set βPβ: Amount of tank filled by 4 pipes in 5 minutes = 80% Amount of tank filled by 4 pipes in 1 minute = 80/5 = 16% For pipes of set βQβ: Amount of tank emptied by 5 pipes in 20 minutes = 60% Amount of tank emptied by 5 pipes in 1 minute = 60/20 = 3% Therefore, effective amount of tank filled by all the pipes of both sets in each minute = 16 β 3 = 13% Therefore, amount of tank filled in 4 minutes = 4 Γ 13 = 52% Therefore, I is true. For II: For pipes of Set βPβ: Amount of tank filled by 4 pipes in 5 minutes = 64% Amount of tank filled by 4 pipes in 1 minute = 64/5 = 12.8% For pipes of set βQβ: Amount of tank emptied by 5 pipes in 20 minutes = 60% Amount of tank emptied by 5 pipes in 1 minute = 60/20 = 3% Therefore, effective amount of tank filled by all the pipes of both sets in each minute = 12.8 β 3 = 9.8% Therefore, amount of tank filled in 4 minutes = 4 Γ 9.8 = 39.2% Therefore, II is false. For III: For pipes of Set βPβ: Amount of tank filled by 4 pipes in 5 minutes = 75% Amount of tank filled by 4 pipes in 1 minute = 75/5 = 15% For pipes of set βQβ: Amount of tank emptied by 5 pipes in 20 minutes = 60% Amount of tank emptied by 5 pipes in 1 minute = 60/20 = 3% Therefore, effective amount of tank filled by all the pipes of both sets in each minute = 15 β 3 = 12% Therefore, amount of tank filled in 4 minutes = 4 Γ 12 = 48% Therefore, III is true
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