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?
Answer & explanation
Correct answer: option 3
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.