Radha sold a watch for Rs. 144 and made a profit percentage equal to the cost…

When the profit percentage on an item equals the cost price (in rupees) itself, the cost price and selling price are related by a quadratic equation: if Cost Price = x, then Profit% = x, so Profit = x × (x/100) = x2/100, and Selling Price = x + x2/100.

1. Let the cost price of the watch be Rs. x. It is given that the profit percentage equals the value of the cost price, so Profit% = x.

2. Profit amount = x% of x = x × (x/100) = x2/100.

3. Selling Price = Cost Price + Profit = x + x2/100. Since the Selling Price = Rs. 144, we get x + x2/100 = 144.

4. Multiplying both sides by 100: 100x + x2 = 14400, i.e. x2 + 100x − 14400 = 0.

5. Solving using the quadratic formula: x = [−100 ± √(1002 + 4×14400)] / 2 = [−100 ± √67600] / 2 = [−100 ± 260] / 2.

6. This gives x = 80 or x = −180. Since the cost price cannot be negative, x = 80.

Verification: taking Cost Price = Rs. 80, the profit percentage = 80, so Profit = 80 × 80/100 = Rs. 64, giving Selling Price = 80 + 64 = Rs. 144 — matching the value given in the question.

Therefore, the cost price of the watch is Rs. 80.