A man invests $\text{Rs. }5000$ at a rate of $6\%$ per annum. How much more should he invest at a rate of $9\%$, so that he can earn a total of $7\%$ per annum?

Let the additional amount invested at $9\%$ be $\text{Rs. }x$.
According to the problem, the total annual interest earned from both investments combined must equal $7\%$ of the entire principal:

$$\frac{5000\times 6\times 1}{100}+\frac{x\times 9\times 1}{100}=\frac{(5000+x)\times 7\times 1}{100}$$

$$30000+9x=7(5000+x)$$

$$30000+9x=35000+7x$$

$$9x-7x=35000-30000$$

$$2x=5000$$

$$x=2500$$

Alternatively, using the rule of allegation:

$$\frac{\text{Amount at }6\%}{\text{Amount at }9\%}=\frac{9-7}{7-6}=\frac{2}{1}$$

Given that the amount invested at $6\%$ is $\text{Rs. }5000$:

$$\frac{5000}{\text{Amount at }9\%}=\frac{2}{1}⟹\text{Amount at }9\%=\frac{5000}{2}=\text{Rs. }2500$$