A ball is projected vertically upward with an initial velocity of...

Distance covered by ball $A$ is $h = 50\left(2\right) - \dfrac{1}{2} \times 10 \times {2}^{2}$$= 100 - 20 = 80m$

Now, at time $t = 2s$, velocity of $A$ is ${v}_{A} = 50 - 10 \times 2 = 30m{s}^{- 1}$

Relative velocity of both balls after $2s$ is ${v}_{rel} = 50 - 30 = 20m{s}^{- 1}$

Here, relative displacement ${x}_{rel} = 80m{s}^{- 1}$ and relative acceleration${a}_{rel} = 0$.

Time taken $t = \dfrac{80}{20} = 4s$

Time at which they will meet is $t = 4 + 2 = 6s$