Two water taps together can fill a tank in 8 8/9 hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank…

Let tap of smaller diameter takes x hours to fill the tank. ∴ tap of larger diameter takes $\displaystyle \mathrm{x}-4$ hours to fill the tank. $\displaystyle \frac{1}{x}+\frac{1}{x-4}=\frac{9}{80}$ $\displaystyle \Rightarrow 9 x^{2}-196 x+320=0$ $\displaystyle \Rightarrow(x-20)(9 x-16)=0$ $\displaystyle \Rightarrow x=20, \frac{16}{9}$ $\displaystyle x=\frac{16}{9}($ rejected $\displaystyle )$ $\displaystyle \therefore x=20$ Hence, tap of smaller diameter and larger diameter takes $\displaystyle 20$ hours & $\displaystyle 16$ hours respectively, to fill the tank.