A book vendor sold a book at loss of 10%. Had he sold it for Rs. 108 more, he…

For a cost price CP, selling at a loss of l% gives a selling price of CP × (1 − l/100), while selling at a profit of p% gives CP × (1 + p/100). The difference between these two hypothetical selling prices always equals CP × (p + l)/100 — the combined percentage swing between the loss and profit outcomes.

1. Let the cost price be Rs. x.

2. A loss of 10% gives a selling price of 0.9x.

3. A profit of 10% gives a selling price of 1.1x.

4. The difference between the two selling prices is 1.1x − 0.9x = 0.2x, and this equals Rs. 108.

5. Solving 0.2x = 108 gives x = 540.

Check: at x = Rs. 540, the loss-price is 0.9 × 540 = Rs. 486 and the profit-price is 1.1 × 540 = Rs. 594; their difference, 594 − 486 = Rs. 108, matches the given data, confirming the cost price.