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A tank can be filled using pipes A, B, and C and can be emptied using pipe D. Pipes A & B can together fill the tank in 8 hours, pipes B & C can together fill the tank in 10 hours and pipes A & C can together fill the tank in 6 hours. If pipe D can alone empty the tank in 15 hours, in how much time will the tank be filled if all the pipes are simultaneously opened?

A tank can be filled using pipes A, B, and C and can be emptied using pipe D. Pipes A & B can together fill the tank in 8 hours, pipes B & C can together fill the tank in 10 hours and pipes A & C can together fill the tank in 6 hours. If pipe D can alone empty the tank in 15 hours, in how much time will the tank be filled if all the pipes are simultaneously opened? Correct Answer 240/31 hrs.

Part filled by pipes A & B in 1 hr. = 1/8

Part filled by pipes B & C in 1 hr. = 1/10

Part filled by pipes A & C in 1 hr. = 1/6

When we add the above 3 equations, each pipe had worked for 2 hrs,

⇒ Part filled by pipes A, B & C in 2 hrs. = 1/8 + 1/10 + 1/6 = 47/120

⇒ Part filled by pipes A, B & C in 1 hr. = 1/2 × 37/120 = 47/240

Part emptied by pipe D in 1 hr. = 1/15

Now, when all pipes are simultaneously opened,

Part filled in 1 hr. = 47/240 - 1/15 = 31/240

∴ The tank will be filled in 240/31 hrs.

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