Say the smaller tap fill the tank in x hours
and the bigger tap fill the tank in (x-10) hours
Therefore in 1 hour the small tap can fill 1/x part of the tank.
and, in 1 hour the small tap can fill 1/(x-10) part of the tank.
Two water taps together can fill a tank in 75/8 hours
So,, in one hour the taps fill 8/75 portion of the tank. so the equation will be,
1/(x) + 1/(x-10) = 8/75
=>4x^2 - 115x + 375 = 0 (solving eventually)
so, solving the equation we will get X = 15/4 and 25
so, if, x =15/4 than (x-10)= -25/4 (it is not possible because time cant be negative)
If x=25 than (x-10) = 15
thus, the smaller tap fills the tank in 25 hours where the large tap fills it in 15 hours.