If $7\%$ of S.P. is equal to $8\%$ of C.P. and if $9\%$ of S.P. is Rs. 2 more than $10\%$ of C.P., then find C.P. and S.P.:

Let Selling Price be $S$ and Cost Price be $C$.
From the first condition:

$$7\%\text{ of }S=8\%\text{ of }C$$

$$\frac{7}{100}S=\frac{8}{100}C⟹7S=8C⟹S=\frac{8}{7}C\text{— (Equation 1)}$$

From the second condition:

$$9\%\text{ of }S=10\%\text{ of }C+2$$

$$\frac{9}{100}S-\frac{10}{100}C=2⟹9S-10C=200\text{— (Equation 2)}$$

Substitute $S=\frac{8}{7}C$ from Equation 1 into Equation 2:

$$9\left(\frac{8}{7}C\right)-10C=200$$

$$\frac{72}{7}C-10C=200$$

$$\frac{72C-70C}{7}=200$$

$$\frac{2C}{7}=200$$

$$2C=1400⟹C=700$$

Now, find $S$ using Equation 1:

$$S=\frac{8}{7}\times 700=800$$

Thus, $\text{C.P.}=700$ and $\text{S.P.}=800$.