Avishek sells a book at a profit of $20\%$. If he had bought it at $20\%$ less and sold it for $\text{Rs. }18$ less, he would have gained $25\%$. The cost price of the book is:

Let the initial cost price (${\text{CP}}_1$) of the book be $x$.
Since it is sold at a profit of $20\%$, the initial selling price (${\text{SP}}_1$) is:

$${\text{SP}}_1=1.20x$$

According to the given conditions:

* New cost price (${\text{CP}}_2$) is $20\%$ less:

$${\text{CP}}_2=x-0.20x=0.80x$$

* New selling price (${\text{SP}}_2$) is $\text{Rs. }18$ less:

$${\text{SP}}_2=1.20x-18$$

The profit gain on the new cost price is $25\%$. Therefore:

$${\text{SP}}_2={\text{CP}}_2\times \left(1+\frac{25}{100}\right)$$

$$1.20x-18=0.80x\times 1.25$$

$$1.20x-18=1.00x$$

$$1.20x-1.00x=18$$

$$0.20x=18$$

$$x=\frac{18}{0.20}=90$$

Thus, the cost price of the book is $\text{Rs. }90$.