Amal and Bimal started a business. Amal invested $\text{Rs. }500$ for $9\text{ months}$ and Bimal invested some money for $6\text{ months}$. If they make a profit of $\text{Rs. }69$ in a year and Bimal gets profit share of $\text{Rs. }46$. The capital of Bimal in the business is

Total profit earned $=\text{Rs. }69$.
Bimal's share of profit $=\text{Rs. }46$.
Therefore, Amal's share of profit $=69-46=\text{Rs. }23$.

The ratio of their profit splits is:

$$\frac{\text{Profit of Amal}}{\text{Profit of Bimal}}=\frac{23}{46}=\frac{1}{2}$$

We know that profit sharing ratios are directly proportional to the product of investment capital and duration:

$$\frac{{\text{Capital}}_{\text{Amal}}\times {\text{Time}}_{\text{Amal}}}{{\text{Capital}}_{\text{Bimal}}\times {\text{Time}}_{\text{Bimal}}}=\frac{{\text{Profit}}_{\text{Amal}}}{{\text{Profit}}_{\text{Bimal}}}$$

Let Bimal's capital be $x$:

$$\frac{500\times 9}{x\times 6}=\frac{1}{2}$$

$$\frac{4500}{6x}=\frac{1}{2}$$

$$6x=9000⟹x=1500$$

Bimal's capital investment is $\text{Rs. }1,500$.