When the price of rice increases by $12\frac{1}{2}\%$, a man can get $250\text{gm}$ less rice for $\text{Rs. }18$. Find the present cost of rice per kg.

Let the original price of rice per kg be $\text{Rs. }x$.
The increase in price is $12\frac{1}{2}\%=\frac{25}{2}\%=\frac{1}{8}$.

$$\text{Present Price}=x\times \left(1+\frac{1}{8}\right)=\frac{9x}{8}$$

According to the question, the difference in the quantity of rice bought for $\text{Rs. }18$ is $250\text{gm}=\frac{250}{1000}\text{kg}=\frac{1}{4}\text{kg}$:

$$\frac{18}{x}-\frac{18}{\frac{9x}{8}}=\frac{1}{4}$$

$$\frac{18}{x}-\frac{16}{x}=\frac{1}{4}$$

$$\frac{2}{x}=\frac{1}{4}$$

$$x=8$$

The original price is $\text{Rs. }8$ per kg.
The present cost of rice per kg is:

$$\text{Present Price}=\frac{9\times 8}{8}=\text{Rs. }9$$