A and B invest $\text{ ₹ }50000$ and $\text{ ₹ 4}5000$ respectively in a business. After 9 months B withdrew his investment. At the end of a year they earned a profit of $\text{ ₹ }13400$. What was B's share of profit?

Given,

Investment of A=$\text{ ₹ }50000$

Investment of B= $\text{ ₹ 4}5000$

Total profit =$\text{ ₹ }13400$

After 9 months B withdrew his investment while A invest for the complete 12 moths. So, ratio of A's profit to B's profit,

$$\begin{gathered} =\frac{50000\times 12}{45000\times 9} \\ =\frac{40}{27} \end{gathered}$$

$\Rightarrow {\mathrm{A}}^{\mathrm{\prime }}\mathrm{s}\text{ profit : }{\mathrm{B}}^{\mathrm{\prime }}\mathrm{s} \text{profit }=40:27$

Profit share's B,

$\begin{array}{l}\mathrm{B}=\frac{27}{(27+40)}\times 13400\\ \mathrm{B}=\frac{27}{67}\times 13400\\ \mathrm{B}=\frac{361800}{67}\\ \mathrm{B}=₹5400\end{array}$

Thus, the correct option is A.