CBSE Class 10 Answered

Let the larger diameter tap fills the tank alone in (x – 10) hours.
 
In 1 hour, the smaller diameter tap can fill 1/x part of the tank.
 
In 1 hour, the larger diameter tap can fill 1/(x – 10) part of the tank.
 
Two water taps together can fill a tank in 75 / 8 hours.
 
But in 1 hour the taps fill 8/75 part of the tank.
 
1 / x  +  1 / (x – 10) = 8 / 75.
 
( x – 10 + x ) / x ( x – 10) =  8 / 75.
 
2( x – 5) / ( x² – 10 x) = 8 / 75.
 
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.
 
But x = 15 / 4 then x – 10 = -25 /4 which is not possible since time
 
But x = 25 then 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.