By selling an article for Rs. 110, a man loses 12%. For how much should he sell it to gain 8%?

Question

Accepted Answer

To determine the correct selling price for the article to gain 8%, we first need to find the cost price of the article. Let's break down the problem step by step:

1. **Finding the Cost Price:**
   - The article is sold for Rs. 110 at a loss of 12%.
   - This means the selling price (SP) is 88% of the cost price (CP) because a 12% loss implies the selling price is 100% - 12% = 88% of the cost price.
   - Therefore, we can set up the equation:  
     $$
     0.88 \times \text{CP} = 110
     $$
   - Solving for CP, we get:  
     $$
     \text{CP} = \frac{110}{0.88} = 125
     $$

2. **Calculating the Selling Price for an 8% Gain:**
   - To gain 8%, the selling price should be 108% of the cost price.
   - Therefore, the new selling price (SP) should be:  
     $$
     \text{SP} = 1.08 \times \text{CP} = 1.08 \times 125 = 135
     $$

3. **Justification for Option 3:**
   - The calculation shows that to achieve an 8% gain, the article should be sold for Rs. 135.
   - Therefore, Option 3, which is Rs. 135, is the correct answer.

4. **Explanation for Why Other Options are Incorrect:**
   - **Option 1 (Rs. 145):** This option suggests a higher selling price than necessary for an 8% gain. Selling at Rs. 145 would result in a gain greater than 8%.
   - **Option 2 (Rs. 120):** This option is too low and would not achieve the desired 8% gain. Selling at Rs. 120 would result in a gain less than 8%.
   - **Option 4 (Rs. 130):** This option is also too low to achieve an 8% gain. Selling at Rs. 130 would result in a gain less than 8%.

In conclusion, based on the calculations and logical reasoning, Option 3 (Rs. 135) is the correct answer for selling the article to gain 8%.