When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe A fill the cistern, if operated separately?

10

A = (x - 5)hrs, B = x  hrs

Efficiency α \(\frac{1}{Time}\)

Therefore, A : B = x : x -5  (Efficiency)

⇒ A + B = x + x - 5 = 2x - 5,

⇒ Time to fill tank = x\(\frac{x-5}{2x - 5}\) = 6,

⇒ \( {x }^{2 } \) - 5x = 12x - 30,

⇒ \( {x }^{2 } \) - 17x + 30 = 0,

⇒ (x - 15)(x - 2) = 0,

⇒ x = 15, 2,

Therefore, Time taken by A to fill the cistern is 15 - 5 = 10 hrs.