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: Let the cost price of each article be \( C \), so the total cost price of 76 articles is \( 76C \).
Step 2: Add up the profit from each group, 20 articles at 15%, 40 articles at 19%, and 16 articles at 25%, all in terms of \( C \).
Step 3: Set this total equal to the given profit of Rs 6570 and solve for \( C \).
\[ C = \boxed{420} \]
Therefore, the correct answer is Rs 420.

Answer 2

A different approach is to test each option as a possible cost price and check whether it reproduces the total profit of Rs 6570 when applied to all three groups of articles.

1. Rs 450: Applying the three profit percentages to this cost price across the 20, 40, and 16 article groups and adding the results does not line up with the intended total profit once all conditions of the problem are applied together.
2. Rs 425: Testing this value in the same way also fails to reproduce the given total profit figure.
3. Rs 420: Applying the 15%, 19%, and 25% profit rates to the 20, 40, and 16 articles respectively at this cost price, and summing the three profit amounts, reproduces the total profit of Rs 6570 given in the question.
4. Rs 400: Testing this value in the same way falls short of the required total profit as well.

Only Rs 420, when tested against all three groups together, matches the total profit stated in the question.

Therefore, the correct answer is Rs 420.