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Two pipes A and B can fill an empty cistern in 32 and 48 hours, respectively. Pipe C can drain the entire cistern in 64 hours when no other pipe is in operation. Initially, when the cistern was empty Pipe A and Pipe C were turned on. After a few hours. Pipe A was turned off and Pipe B was turned on instantly. In all it took 112 hours to fill the cistern. For how many hours was Pipe B turned on?

Two pipes A and B can fill an empty cistern in 32 and 48 hours, respectively. Pipe C can drain the entire cistern in 64 hours when no other pipe is in operation. Initially, when the cistern was empty Pipe A and Pipe C were turned on. After a few hours. Pipe A was turned off and Pipe B was turned on instantly. In all it took 112 hours to fill the cistern. For how many hours was Pipe B turned on? Correct Answer 72

Let the total amount of work be 192 units -------(L.C.M of 32, 48, and 64)

Amount of work done by pipe A in one hour = 192/32 = 6 units

Amount of work done by pipe B in one hour = 192/48 = 4 units

Amount of work done by pipe C in one hour = -192/64 = -3 units

Let Pipe A and Pipe C operate for x hours. After x hours, Pipe A is turned off and Pipe B is turned on. Now Pipe B and Pipe C will operate for remaining 112 – x hours.

Work done by Pipe A and C in x hours = (6 – 3) × x units

Work done by Pipe B and C in (112 – x) hours = (4 – 3) × (112 – x) units.

Total work done should be 192 units.

⇒ (6 – 3) × x + (4 – 3) × (112 – x) = 192

⇒ 3x + 112 – x = 192

⇒ 2x = 80

⇒ x = 40

∴ Pipe B was turned on for 112 – 40 = 72 hours.

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