A book vendor sold a book at a loss of $10\%$. Had he sold it for $\text{₹}1,080$ more, he would have earned a profit of $10\%$. Find out the cost of the book.

Let the cost price ($\text{CP}$) of the book be $x$.
* Initial condition: Sold at $10\%$ loss $⟹{\text{SP}}_1=90\%\text{ of }x=0.9x$
* Second condition: Sold at $10\%$ profit $⟹{\text{SP}}_2=110\%\text{ of }x=1.1x$

The difference between the two selling prices is given as $\text{₹}1,080$:

$${\text{SP}}_2-{\text{SP}}_1=1080$$

$$1.1x-0.9x=1080$$

$$0.2x=1080$$

$$x=\frac{1080}{0.2}=\frac{10800}{2}=5400$$

Thus, the cost price of the book is $\text{₹}5,400$.