Profit earned by selling an article for ₹1060 is 20% more than the loss…

Profit and loss are both measured against the cost price (CP) of an article: Profit = Selling Price − CP (when SP is greater than CP), and Loss = CP − Selling Price (when CP is greater than SP). When the same article is sold at two different prices, one giving a profit and the other giving a loss, the unknown cost price can be found by expressing both amounts in terms of CP and using the relationship stated between them.

1. Let the cost price of the article be x.

2. Selling at ₹950 (below x) gives a loss of x − 950.

3. Selling at ₹1060 (above x) gives a profit of 1060 − x.

4. The profit is 20% more than the loss: 1060 − x = 1.2 × (x − 950).

5. Expanding: 1060 − x = 1.2x − 1140.

6. Collecting terms: 1060 + 1140 = 1.2x + x, so 2200 = 2.2x.

7. Solving: x = 1000. So the cost price is ₹1000.

8. To earn a 20% profit on this cost price, the selling price must be 1000 × 1.2 = ₹1200.

Check: with CP = ₹1000, selling at ₹1060 gives a profit of ₹60, and selling at ₹950 gives a loss of ₹50. Since ₹50 × 1.2 = ₹60, the profit is indeed 20% more than the loss, confirming CP = ₹1000 is correct — so the selling price needed for a 20% profit is ₹1200.