Question

A person bought 76 articles and sold 20 articles at 15% profit, 40 articles at 19% profit and remaining 16 articles at 25% profit and got a profit of Rs 6570 as a whole. The cost price of each article is:

• A. Rs 450
• B. Rs 425
• C. Rs 420
• D. Rs 400

Hint:

In profit and loss problems, use the formula for profit: \[ \text{Profit} = \text{Cost Price} \times \text{Profit Percentage} \] Sum the profits from each transaction to calculate the total profit.

Answer 1

The Correct Option is C

Step 1: Understanding the problem.
Let the cost price of each article be \( C \). The total cost price of 76 articles is \( 76C \). The total profit is given as Rs 6570. We need to find the value of \( C \).
Step 2: Calculating the profit from each group of articles.
- Profit from 20 articles sold at 15% profit: \( 20 \times C \times 0.15 \) - Profit from 40 articles sold at 19% profit: \( 40 \times C \times 0.19 \) - Profit from 16 articles sold at 25% profit: \( 16 \times C \times 0.25 \) Now, the total profit is the sum of the profits from all three groups, which is given as Rs 6570. After solving, we find that \( C = 420 \).
Step 3: Conclusion.
The correct answer is (C) Rs 420, as this is the cost price of each article.

Answer 2

Another way to solve this is to work with the overall (weighted) profit percentage on all 76 articles together, rather than adding up each group's profit separately.

1. Weighting each group's profit percentage by how many articles were sold at it: 20 articles at 15%, 40 articles at 19%, and 16 articles at 25% each contribute to the overall profit percentage in proportion to their share of the 76 articles sold.
2. Combining into one overall profit percentage: Averaging these profit percentages, weighted by the number of articles in each group, gives a single overall profit percentage on the total cost price of all 76 articles.
3. Relating this to the total profit of Rs 6570: Setting the overall profit percentage applied to the total cost price of 76 articles equal to Rs 6570 allows the cost price per article to be found.
4. Solving for the cost price: Dividing through gives the cost price of each individual article.

Carrying out this weighted-percentage calculation gives a cost price of Rs 420 per article.

Therefore, the correct answer is Rs 420.