An Increase of 3 in the selling price of an article turns a loss of7 `1/2`% into a gain of 7 `1/2` %. The cost price (in) of the article is:

Options

A. 25
B. 20
C. 15
D. 10

Answer

To solve the problem step by step, we need to determine the cost price of the article based on the information given about the selling price and the percentage loss and gain.

### Step-by-Step Solution:

1. **Understand the Problem**:
We know that an increase of 3 in the selling price changes a loss of 7.5% into a gain of 7.5%.

2. **Convert Percentages to Fractions**:
The loss of 7.5% can be expressed as a fraction:
\[ \text{Loss} = \frac{7.5}{100} = \frac{15}{200} = \frac{15}{2} \% \]
Similarly, the gain of 7.5% is:
\[ \text{Gain} = \frac{7.5}{100} = \frac{15}{200} = \frac{15}{2} \% \]

3. **Calculate the Total Change in Percentage**:
The change from a loss to a gain means we need to add the absolute values of the loss and gain:
\[ \text{Total Change} = 7.5\% + 7.5\% = 15\% \]

4. **Relate the Change to the Increase in Selling Price**:
The problem states that this total change corresponds to an increase of 3 in the selling price. Therefore, we can set up the equation:
\[ 15\% \text{ of Cost Price} = 3 \]

5. **Express the Cost Price in Terms of the Increase**:
Let the cost price be \( CP \). Then:
\[ \frac{15}{100} \times CP = 3 \]

6. **Solve for the Cost Price**:
Rearranging the equation gives:
\[ CP = \frac{3 \times 100}{15} = \frac{300}{15} = 20 \]

7. **Conclusion**:
The cost price of the article is \( \text{CP} = 20 \).

### Final Answer:
The cost price of the article is **20**.

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