Question

The cost price of 25 articles is the same as the selling price of `m' articles. If the profit is 25%, then what is the value of `m'?

• A. 18
• B. 16
• C. 25
• D. 20

Hint:

Shortcut Formula: If CP of \(x\) items = SP of \(y\) items, then \(\text{Profit %} = \frac{x-y}{y} \times 100\). Here: \(25 = \frac{25-m}{m} \times 100 \implies m = 20\).

Answer 1

The Correct Option is D

Step 1: Set up the Equation:
Let \(CP\) be the cost price of 1 article and \(SP\) be the selling price of 1 article. Given: \(25 \times CP = m \times SP\). Rearranging gives the ratio: \[ \frac{SP}{CP} = \frac{25}{m} \] Step 2: Use the Profit Formula:
We are given a Profit % of 25%. \[ \text{Profit %} = \left( \frac{SP}{CP} - 1 \right) \times 100 \] \[ 25 = \left( \frac{25}{m} - 1 \right) \times 100 \] Step 3: Solve for m:
Divide by 100: \[ 0.25 = \frac{25}{m} - 1 \] \[ 1.25 = \frac{25}{m} \] \[ m = \frac{25}{1.25} = \frac{2500}{125} \] \[ m = 20 \]