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A set A of 6 pipes can fill the 60% of the tank in 6 minutes, another set B of 5 pipes can fill ¼ of the same tank in 4 minutes and a third set C of 4 pipes can empty ½ of the same tank in 8 minutes. If the efficiency of 2 pipes among the third set of pipes is increased to twice then find the per minute rate (in %) at which the tank will be full completely if all these 15 pipes are opened together?

A set A of 6 pipes can fill the 60% of the tank in 6 minutes, another set B of 5 pipes can fill ¼ of the same tank in 4 minutes and a third set C of 4 pipes can empty ½ of the same tank in 8 minutes. If the efficiency of 2 pipes among the third set of pipes is increased to twice then find the per minute rate (in %) at which the tank will be full completely if all these 15 pipes are opened together? Correct Answer 6.875%

Since set A of 6 pipes can fill 60% of the tank in 6 minutes

⇒ Set A can fill 10% of the tank in 1 minute

Since set B of 5 pipes can fill ¼ of the tank in 4 minutes

⇒ Set B can fill 6.25% (100/(4 × 4)%) of the tank in 1 minute

Since set C of 4 pipes can empty ½ of the tank in 8 minutes

⇒ Set C can empty 6.25% (100/(2 × 8)%) of the tank in 1 minute

⇒ Each pipe in set C can empty 1.5625% of the tank in 1 minute

When efficiency of 2 pipes in set C becomes twice

⇒ 2 pipes from set C can empty (1.5625 × 2%) = 3.125% of the tank in 1 minute

⇒ Efficiency of these two pipes increased as twice ∴  2 × 3.125 = 6.25

⇒ Another 2 pipes from set C can empty (3.125%) of the tank in 1 minute

If all 15 pipes are opened together

⇒ The per minute rate = 10% + 6.25% - 6.25 - 3.125%= 6.875%

∴ the per minute rate (in %) at which the tank will be full completely if all these 15 pipes are opened together = 6.875%

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