It takes two pipes X and Y, running together, to fill a tank in 6 minutes. It takes A 5 minutes less than Y to fill the tank, then what will be the time taken by Y alone to fill the tank?

Question: It takes two pipes X and Y, running together, to fill a tank in 6 minutes. It takes A 5 minutes less than Y to fill the tank, then what will be the time taken by Y alone to fill the tank?

Solution:
Let the time taken by pipe X to fill the tank be a minutes
Time is taken by pipe Y to fill the tank = a + 5 minutes

So,
⇒ (1/a) + {1/(a + 5)} = 1/6
⇒ (2a + 5)/a(a + 5) = 1/6
⇒ a² + 5a - 12a - 30 = 0
⇒ a² - 7a - 30 = 0
⇒ (a - 10)(a + 3) = 0
⇒ a = 10, - 3
∴ a = 10 ; [neglecting the negative value of a]

Thus, time taken by Y alone to fill the tank is 10 + 5 = 15 minutes