A person sold an article for Rs. 3600 and got a profit of 20%. Had he sold the article for Rs. 3150, how much profit would he have got ?

Question

Accepted Answer

To determine the profit percentage if the article was sold for Rs. 3150, we first need to find the cost price of the article.

1. **Finding the Cost Price:**
   - The article was sold for Rs. 3600 with a profit of 20%.
   - Let the cost price be $ C $.
   - Profit percentage is calculated as: $\text{Profit} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100\%$.
   - Given: $\frac{3600 - C}{C} \times 100 = 20$.
   - Simplifying, we get: $3600 - C = 0.2C$.
   - Therefore, $3600 = 1.2C$.
   - Solving for $ C $, we get: $C = \frac{3600}{1.2} = 3000$.

2. **Calculating Profit for Selling Price of Rs. 3150:**
   - New selling price = Rs. 3150.
   - Profit = Selling Price - Cost Price = 3150 - 3000 = Rs. 150.
   - Profit percentage = $\frac{\text{Profit}}{\text{Cost Price}} \times 100\%$.
   - Profit percentage = $\frac{150}{3000} \times 100 = 5\%$.

3. **Justification for Option 2:**
   - The calculated profit percentage when the article is sold for Rs. 3150 is 5%.
   - Therefore, Option 2, which states a profit of 5%, is correct.

4. **Explanation for Incorrectness of Other Options:**
   - **Option 1 (4%):** If the profit percentage were 4%, the profit would be $\frac{4}{100} \times 3000 = 120$. This would imply a selling price of $3000 + 120 = 3120$, which is not the case.
   - **Option 3 (6%):** If the profit percentage were 6%, the profit would be $\frac{6}{100} \times 3000 = 180$. This would imply a selling price of $3000 + 180 = 3180$, which is not the case.
   - **Option 4 (10%):** If the profit percentage were 10%, the profit would be $\frac{10}{100} \times 3000 = 300$. This would imply a selling price of $3000 + 300 = 3300$, which is not the case.

Thus, the correct answer is Option 2, which is a profit of 5%.