Question

The cost price of \(20\) articles is the same as the selling price of \(x\) articles. If the profit is \(25%\), then the value of \(x\) is:

• A. \(15\)
• B. \(16\)
• C. \(18\)
• D. None of these

Hint:

In profit-loss problems, always adjust selling price using the given percentage profit or loss before equating totals.

Answer 1

The Correct Option is B

Step 1 (Define cost price per article).
Let cost price of \(1\) article = \(C\).
Therefore, cost price of \(20\) articles = \(20C\).
Step 2 (Define selling price per article using profit).
Profit \(= 25%\) Selling Price (SP) of 1 article = \(C + 0.25C = 1.25C\).
Step 3 (Set up equation using given condition).
Given: Cost price of \(20\) articles = Selling price of \(x\) articles.
\[ 20C = x \times 1.25C \] Step 4 (Simplify the equation).
Cancel \(C\) from both sides: \[ 20 = 1.25x \] \[ x = \frac{20}{1.25} = 16 \] Step 5 (Conclusion).
Hence, \(x = 16\), which matches Option 2.
\[ \boxed{16\ \text{(Option (b)}} \]