Lets denote $\text{CP}_x$ and $\text{SP}_x$ for per unit Cost Price and Selling Price respectively for year $x.$ Given that
$ \frac{1}{3}\text{CP}_1 = \frac{1}{2}\text{CP}_2 = \text{CP}_3 =$ ₹$~1$
$\quad \implies \text{CP}_2 =$ ₹$~2,\text{CP}_3 =$ ₹$~1$
Net profit for year $2$ is given by
$\text{SP}_2 – (200*\text{CP}_2 + 0.13*\text{SP}_2) = 296 $
$\quad \implies 0.87*\text{SP}_2 = 296 + 200*2 = 696$
$\quad \implies \text{SP}_2 = \frac{696}{0.87} =$ ₹$~800 \qquad \qquad \qquad \to (i)$
Net profit for year $3$ is given by
$\text{SP}_3 – (300*\text{CP}_3 + 0.15*\text{SP}_2) = 210 $
$\quad \implies 0.85*\text{SP}_3 = 210 + 300*1 = 510$
$\quad \implies \text{SP}_3 = \frac{510}{0.85} =$ ₹$~600 \qquad \qquad \qquad \to (ii)$
$(i)\div(ii) \implies \frac{\text{SP}_2}{\text{SP}_3} = \frac{800}{600} = \frac{4}{3}$
Ans: A. $4:3$