Question

A shopkeepers marked price of an article is 140% of the cost price. He sold the articles under two schemes. Scheme 1 is to sell each article at a discount of 10% and scheme 2 to sell two articles at a discount of 15% each. He sold 60% of the articles under scheme 2 and the remaining under scheme 1. What is his overall gain or loss percentage?

• A. 0.08%loss
• B. 11.8%gain
• C. 13.6%gain
• D. 21.8%gain
• E. 23.6%gain

Answer 1

The Correct Option is D

To determine the overall gain or loss percentage, we need to follow these steps:

1. Let's assume the cost price (CP) of each article is x.
2. The marked price (MP) of the article is 140% of the cost price. Therefore,
   \text{MP} = 1.4x.
3. Scheme 1: In this scheme, articles are sold at a 10% discount on the marked price.
   Selling price (SP) under Scheme 1 can be calculated as:
   \text{SP}_{\text{Scheme 1}} = \text{MP} - 10\% \times \text{MP} = 1.4x - 0.1 \times 1.4x = 1.26x.
4. Scheme 2: In this scheme, two articles are sold at a 15% discount each on the marked price.
   Selling price for one article in Scheme 2 is:
   \text{SP}_{\text{Scheme 2}} = \text{MP} - 15\% \times \text{MP} = 1.4x - 0.15 \times 1.4x = 1.19x.
5. Suppose the total number of articles is 100 (for calculation simplicity).
6. Under Scheme 2, 60% of the articles are sold. Therefore, the number of articles sold in Scheme 2 is 60 articles.
   Total SP from Scheme 2:
   60 \times 1.19x = 71.4x.
7. The remaining 40% of the articles are sold under Scheme 1. Number of articles: 40.
   Total SP from Scheme 1:
   40 \times 1.26x = 50.4x.
8. Total SP from both schemes is:
   71.4x + 50.4x = 121.8x.
9. Total CP of all 100 articles is: 100 \times x = 100x.
10. The profit is the difference between total SP and total CP,
    Profit = 121.8x - 100x = 21.8x.
11. The overall gain percentage is:
    \left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100 = \left( \frac{21.8x}{100x} \right) \times 100 = 21.8\%.
12. Thus, the shopkeeper makes a 21.8% gain. Therefore, the correct answer is: 21.8% gain.