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Three similar red coloured pipes can together fill the tank in 2 hours and two similar blue coloured pipes can together empty the tank in 6 hours. If one red and one blue pipe is opened in the tank simultaneously, in how much time will the tank be filled?

Three similar red coloured pipes can together fill the tank in 2 hours and two similar blue coloured pipes can together empty the tank in 6 hours. If one red and one blue pipe is opened in the tank simultaneously, in how much time will the tank be filled? Correct Answer 12 hours

Part filled by 3 red pipes in 1 hr. = 1/2

Part filled by 1 red pipe in 1 hr. = 1/3 × 1/2 = 1/6

Part emptied by 2 blue pipes in 1 hr. = 1/6

Part emptied by 1 blue pipe in 1 hr. = 1/2 × 1/6 = 1/12

When 1 red and 1 blue pipe are opened simultaneously,

Part filled in 1 hr. = 1/6 – 1/12 = 1/12

∴ The tank will be filled in 12 hours.

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