Question

If the selling price of 40 articles is same as the cost price of 50 articles, then the loss or gain percent is

• A. (20
• B. (20
• C. (25
• D. (25

Hint:

An incredibly fast mental shortcut rule for these styles of question templates is: \[ \text{Gain or Loss Percentage} = \left( \frac{\text{Number of CP articles} - \text{Number of SP articles}}{\text{Number of SP articles}} \right) \times 100 \] Substituting the values gives: (50 - 4040 100

Answer 1

The Correct Option is D

Step 1: Pin down the basic idea.
In profit and loss, gain or loss is found by comparing selling price with cost price for the same set of goods. We will use one article as our unit.

Step 2: Set a convenient cost.
Let the cost price of one article be $1$ rupee. Then the cost of $50$ articles is $50$ and the cost of $40$ articles is $40$.

Step 3: Use the given equality.
We are told the selling price of $40$ articles equals the cost price of $50$ articles. So the money got for $40$ articles is $50$.

Step 4: Find selling price per article.
\[ \text{SP of one} = \frac{50}{40} = 1.25 \] Since this is more than the cost of $1$, there is a gain.

Step 5: Compute the gain on one article.
Gain per article $= 1.25 - 1 = 0.25$. The cost per article is $1$.

Step 6: Convert to percentage.
\[ \text{Gain }\% = \frac{0.25}{1}\times 100 = 25\% \] So there is a gain of \[ \boxed{25\% \text{ gain}} \]