Two taps open into a tank. If both are opened, the tank would be filled in 12 minutes. The time taken to fill the tank by the smaller tap alone is 10 minutes more than the time taken of fill it by the larger tap alone. If the smaller tap alone is opened, what would be the time taken to fill the tank?

Let the time taken by the larger tap alone to fill the tank be x minutes.

∴ Tank filled in 1 minute =

time taken by smaller tap to fill the tank alone = x + 10.

∴ Tank filled in 1 minute =

time taken by both of the taps to fill the tank = 12 minute.

Now in 1 minute they both will fill ^th of the tank.

⇒

⇒ (2x + 10)12 = x² + 10x

⇒ x² + 10x – 24x – 120 = 0

⇒ x² – 14x – 120 = 0

⇒ (x–20)(x + 6)

time cannot be negative so 20 minutes for larger tap

and 30 minutes for smaller tap.