Two water taps together can fill a tank in hours. The larger tap takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

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.


25