The cost price of 40 magazines is equal to the selling price of P magazines of the same kind. If the profit made on the sale is 25 percent, what is the value of P?

Introduction / Context:
This question evaluates understanding of the relationship between cost price and selling price when profit is given. It uses an equation linking the cost of several items to the selling price of a different number of items. The structure is similar to other standard profit percentage questions seen in competitive exams.

Given Data / Assumptions:

• Cost price of 40 magazines together = total CP.
• Selling price of P magazines together = total SP.
• Total CP of 40 magazines = total SP of P magazines.
• Profit earned on each magazine is 25 percent.
• All magazines are identical, and cost price per magazine is constant.

Concept / Approach:
We use variables to represent cost price per magazine and selling price per magazine. The given profit percentage helps us express selling price in terms of cost price. Equating total cost of 40 magazines with total selling price of P magazines yields an equation that can be solved for P.

Step-by-Step Solution:
Let cost price of one magazine be C. Then total cost price of 40 magazines = 40 * C. Given profit percent = 25 percent, so selling price of one magazine S = C * (1 + 25 / 100) = 1.25 * C. Total selling price of P magazines = P * S = P * 1.25 * C. Given: 40 * C = P * 1.25 * C. Divide both sides by C (C is not zero): 40 = 1.25 * P. So P = 40 / 1.25 = 32.

Verification / Alternative check:
Assume C = Rs. 100 for easy verification. Cost of 40 magazines = 40 * 100 = Rs. 4000. Selling price per magazine with 25 percent profit = 100 * 1.25 = Rs. 125. If P = 32, total selling price of 32 magazines = 32 * 125 = Rs. 4000. This equals the total cost of 40 magazines, confirming that P = 32 is correct.

Why Other Options Are Wrong:
40: This would imply no profit and contradict the 25 percent profit condition. 16 and 30: These values do not satisfy the equation 40 = 1.25 * P. Only P = 32 balances total cost price and total selling price correctly under a 25 percent profit.

Common Pitfalls:
A typical mistake is to mix up cost price and selling price or to ignore the profit percentage when forming the equation. Some candidates also attempt to use trial and error instead of using a clear algebraic relationship. Writing down the equation 40 * C = P * 1.25 * C helps avoid such confusion.

Final Answer:
The value of P is 32.