Amal invests $\frac{1}{4}$ of his capital at $8\%$ p.a., $\frac{1}{5}$ at $10\%$ p.a., and the remainder at $7\%$ p.a. If his total annual income from interest is $\text{Rs. }628$, then his total capital is

Let the total capital be $x$.
* First part = $\frac{1}{4}x$, invested at $8\%$
* Second part = $\frac{1}{5}x$, invested at $10\%$
* Remaining part = $x-\left(\frac{1}{4}x+\frac{1}{5}x\right)=x-\frac{9}{20}x=\frac{11}{20}x$, invested at $7\%$

The sum of the interest earned from all parts equals the total annual income:

$$\left(\frac{1}{4}x\times \frac{8}{100}\right)+\left(\frac{1}{5}x\times \frac{10}{100}\right)+\left(\frac{11}{20}x\times \frac{7}{100}\right)=628$$

$$\frac{2x}{100}+\frac{2x}{100}+\frac{77x}{2000}=628$$

To make denominators uniform, convert $\frac{2x}{100}$ to $\frac{40x}{2000}$:

$$\frac{40x+40x+77x}{2000}=628$$

$$\frac{157x}{2000}=628$$

$$157x=628\times 2000$$

Since $628=157\times 4$:

$$x=4\times 2000=\text{Rs. }8000$$