The particles P and Q are projected simultaneously from two towers as shown. They collide in mid air Then d is 

 

$$\begin{gathered} they together travel a horizontal dis\tan ce d and vertical dis\tan ce \left(20 -10\right) in time t \\ verical dis\tan ce travel \frac{1}{2}g{t}^2+10\sqrt{2}\sin {45}^{0}t -\frac{1}{2}g{t}^2=10 solving t=1 \\ horiaontal dis\tan ce travel in 1 sec (10\sqrt{2}\cos {45}^0+10)1=d \\ d=20 m \end{gathered}$$