Two projectiles $A$ and $B$ are fired simultaneously as shown in figure. They collide in air at point at time $t$. Then

$$\begin{gathered} X_A=X_B \\ \therefore 10+(u_1 \cos {\theta }_1)t=20-(u_2 \cos {\theta }_2)t \\ or t(u_1 \cos {\theta }_1+u_2 \cos {\theta }_2)=10 \\ y_A=y_B \\ \therefore 10+(u_1\sin {\theta }_1)t-\frac{1}{2}g{t}^2 \\ =20+(u_2 \sin {\theta }_2)t-\frac{1}{2}g{t}^2 \\ \therefore (u_{1 }\sin {\theta }_1-u_2 \sin {\theta }_2)t=10 \end{gathered}$$