A and B jointly start a business. The investment of A is equal to three times the investment of B. Find the share of A in the annual profit of ₹55204.

The correct option is ₹41,403.

To find the share of A in the annual profit, we need to determine the ratio of the investments made by A and B.

Let the investment of B be represented by:
$x$
According to the problem, the investment of A is equal to three times the investment of B. Therefore, the investment of A is:
$3x$

The ratio of their investments is:
$$\text{Investment of A}:\text{Investment of B}=3x:x=3:1$$

Since both partners invested their capital for the same duration (one year), the annual profit is shared in the same ratio as their investments. Therefore, the profit-sharing ratio between A and B is also:
$3:1$

The total number of parts in the profit-sharing ratio is:
$$3+1=4\text{parts}$$

A's share corresponds to 3 parts out of the total 4 parts. Given that the total annual profit is ₹55,204, we calculate A's share as follows:
$$\text{Share of A}=\frac{3}{4}\times 55204$$

First, we find the value of one part by dividing the total profit by 4:
$$\frac{55204}{4}=13801$$

Next, we multiply this value by 3 to find A's share (which represents 3 parts):
$$3\times 13801=41403$$

Thus, the share of A in the annual profit is ₹41,403.