A man sells a book at a profit of $20\%$. If he had bought it at $20\%$ less and sold it for ₹ 18 less, he would have gained $25\%$. The cost price of the book is (M.A.T., 2009)

### Concept & Successive Profit Scenarios When both Cost Price and Selling Price change, formulate equations for the initial and final states based on $CP$ and $SP$, and apply the new profit percentage to the new $CP$. $$ \text{New SP} = \text{New CP} \times \left(1 + \frac{\text{New Profit } \%}{100}\right) $$ ### Step-by-Step Solution * Let the original Cost Price be $CP = x$. * Initial profit is $20\%$, so original Selling Price $SP = 1.2x$. * The man bought it at $20\%$ less: New $CP = x - 0.2x = 0.8x$. * He sold it for ₹ 18 less: New $SP = 1.2x - 18$. * On this transaction, he gains $25\%$. So, New $SP = \text{New } CP \times 1.25$. * Substitute the expressions: $1.2x - 18 = 0.8x \times 1.25$ * $1.2x - 18 = 1.0x$ * $1.2x - x = 18$ * $0.2x = 18$ * $x = \frac{18}{0.2} = 90$ ### Exam Strategy & Shortcut Use a base of 100 units for CP. Let CP = 100u, SP = 120u. New CP = 80u. New Profit = 25% on 80u = 20u. New SP = 80u + 20u = 100u. The decrease in SP is 120u - 100u = 20u. We are given this decrease is ₹ 18. So, 20u = 18. We need CP, which is 100u. $100u = 18 \times 5 = 90$. ### Common Pitfall Applying the new profit percentage ($25\%$) to the original Cost Price instead of the updated, reduced Cost Price. ### Final Answer Therefore, the correct answer is **₹ 90**.