two water taps together can fill a tank in 9(3/8 ) hours . the tap of the larger diameter takes 10 hours less than smaller one to fill the tank seprately.find the time in which each tap can seprately fill the tank.

Let the tap with smaller diameter fills the tank alone in x hours.
Let the tap with larger diameter fills the tank alone in (x – 10) hours.
 
In 1 hour, the tap with smaller diameter can fill 1/x part of the tank.
In 1 hour, the tap with larger diameter can fill 1/(x – 10) part of the tank.
 
The tank is filled up in 75/8 hours.
Thus, in 1 hour the taps fill 8/75 part of the tank.

 

 
If x = 25, then (x – 10) = 25 – 10 = 15.
 
Thus, the tap with smaller diameter fills the tank alone in 25 hours where as the larger diameter fills the tank alone in 15 hours.

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