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A and B pipes can fill a tank together in 12 hours. If A worked half as efficiently as it usually does and if B worked thrice as efficiently as it usually does then the tank gets filled in 9 hours. How long would it take for pipe A to fill the tank alone completely? 

A and B pipes can fill a tank together in 12 hours. If A worked half as efficiently as it usually does and if B worked thrice as efficiently as it usually does then the tank gets filled in 9 hours. How long would it take for pipe A to fill the tank alone completely?  Correct Answer 18 hours

Both A and B pipes can fill a tank together in 12 hours

⇒ Portion of tank filled in 1 hour by both pipes A and B = 1/12

Let pipe A fill the tank in “a” hours and let pipe B fill the tank in “b” hours

⇒ Portion of tank filled in 1 hour by pipe A = 1/a

⇒ Portion of tank filled in 1 hour by pipe B = 1/b

⇒ 1/a + 1/b = 1/12        …. (1)

If efficiency of pipe A is halved and efficiency of pipe B is thrice then

Both A and B pipes can fill a tank together in 9 hours

⇒ Portion of tank filled in 1 hour by pipe A = 1/2a

⇒ Portion of tank filled in 1 hour by pipe B = 3/b

⇒ 1/2a + 3/b = 1/9        …. (2)

Solving equations (1) and (2) we get

⇒ a = 18 hours and b = 36 hours

∴ It takes 18 hours for pipe A to alone fill the tank

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