The discount given on an article is Rs. 960 more than the profit made on it. The selling price of the article is Rs. 1920, and the shopkeeper marks the article at 100\% above its cost price. What is the profit percentage earned on the article?

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Accepted Answer

**Solution:**

1. Let the cost price of the article be $ C $.

2. Since the article is marked 100\% above cost price, the marked price $$ M = C + 100\% \text{ of } C = 2C $$.

3. The selling price $ S = 1920 $.

4. Let the profit be $ P $. Then, profit = $ S - C = P $.

5. The discount allowed is Rs. 960 more than the profit, so discount $ D = P + 960 $.

6. Discount is also $ M - S $, so:
   $$
   D = M - S = 2C - 1920
   $$

7. Equate the two expressions for discount:
   $$
   P + 960 = 2C - 1920
   $$

8. Substitute $ P = 1920 - C $ into the above:
   $$
   (1920 - C) + 960 = 2C - 1920
   $$

9. Simplify:
   $$
   2880 - C = 2C - 1920
   $$

10. Bring terms involving $ C $ to one side:
    $$
    2880 + 1920 = 2C + C
    $$
    $$
    4800 = 3C
    $$

11. Solve for $ C $:
    $$
    $C = \frac{4800}{3} = 1600$
    $$

12. Calculate profit $ P = 1920 - 1600 = 320 $.

13. Profit percentage:
    $$
   $ \text{Profit \%} = \frac{P}{C} \times 100 = \frac{320}{1600} \times 100 = 20\%$ 
    $$

**Answer:** 20\%

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