In this paper, we prove common fixed point theorems for a pair of mappings satisfying rational inequality. Also, we prove common fixed point theorems for weakly compatible maps, weakly compatible along with (CLR) and E. A. properties that generalizes the results of Sintunavarat et al. [15]. Further, we apply our results to find the solution of Urysohn integral equations \begin{align*} x(t)&=ıt^b_aK_1(t,s,x(s))ds+g(t), x(t)&=ıt^b_aK_2(t,s,x(s))ds+h(t), \end{align*} where $t\in[a,b]\subseteq\mathbb R,x,g,h\in X$ and $K_1,K_2\colon[a,b]\times[a,b]\times\mathbb R^n\to\mathbb R^n$.