$${1 \over 2}mv_1^2 = {1 \over 2}\left( {{1 \over 2}m{u^2}} \right)$$

$$ \Rightarrow $$ $$v_1^2 = {{{u^2}} \over 2}$$

$$ \Rightarrow $$ $${v_1} = {u \over {\sqrt 2 }}$$ ......(1)

Also collision is elastic : k_i = k_f

$${{1 \over 2}m{u^2} = {1 \over 2}mv_1^2 + {1 \over 2}\left( {10m} \right)v_2^2}$$

$$ \Rightarrow $$ $${{1 \over 2} \times {1 \over 2}m{u^2} = {1 \over 2}\left( {10m} \right)v_2^2}$$

$$ \Rightarrow $$ $${v_2^2 = {{{u^2}} \over {20}}}$$

$$ \Rightarrow $$ $${v_2} = {u \over {\sqrt {20} }}$$

By momentum conservation along y :

m₁v₁sin $$\theta $$₁ = m₂v₂sin $$\theta $$₂

$$ \Rightarrow $$ mv₁sin $$\theta $$₁ = 10mv₂sin $$\theta $$₂

$$ \Rightarrow $$ $${u \over {\sqrt 2 }}$$sin $$\theta $$₁ = 10 $$ \times $$ $${u \over {\sqrt {20} }}$$sin $$\theta $$₂

$$ \Rightarrow $$ sin $$\theta $$₁ = $$\sqrt {10} $$ sin $$\theta $$₂

$$ \therefore $$ n = 10