Two water taps to

Let the tap of the smaller diameter and larger diameter fills the tank alone in x and (x – 10) hours respectively.

In 1 hour, the tap of the smaller diameter can fill 1/x part of the tank.

In 1 hour, the tap of the larger diameter can fill 1/(x – 10) part of the tank.

Two water taps together can fill a tank in hours = 75/ 8 hours.

But in 1 hour the taps fill 8/75 part of the tank.

⇒

⇒

⇒ 4x² – 40x = 75x – 375

⇒ 4x² – 115x + 375 = 0

⇒ 4x² – 100x – 15x + 375 = 0

⇒ 4x(x – 25) – 15( x – 25) = 0

⇒ (4x -15)( x – 25) = 0

⇒ x = 25, 15/4

Taking x = 15 / 4

⇒ x – 10 = -25 /4 (But, time cannot be negative)

Now, taking x = 25

⇒ x – 10 = 15

Larger diameter of the tap can the tank 15 hours and smaller diameter of the tank can fill

the tank in 25 hours.