On the selling an article for Rs 19.50, a man gains 30%. In order to gain 40%, what will be the increase in its selling price?

Options

A. 1.95
B. 1.75
C. 1.5
D. 2

Answer

To solve the problem step by step, we need to find the increase in the selling price of an article when the gain changes from 30% to 40%.

### Step-by-Step Solution:

1. **Identify the Selling Price and Gain Percentage:**
- The selling price (SP) of the article is Rs. 19.50.
- The gain percentage is initially 30%.

2. **Calculate the Cost Price (CP):**
- If the selling price represents 130% of the cost price (because 100% + 30% = 130%), we can set up the equation:
\[ 130\% \text{ of CP} = 19.50 \]
- This can be written as:
\[ \frac{130}{100} \times CP = 19.50 \]
- To find CP, rearrange the equation:
\[ CP = \frac{19.50 \times 100}{130} \]

3. **Calculate CP:**
- Now, calculate the value:
\[ CP = \frac{19.50 \times 100}{130} = \frac{1950}{130} = 15 \]
- So, the cost price (CP) of the article is Rs. 15.

4. **Calculate the New Selling Price for 40% Gain:**
- To gain 40%, the selling price will represent 140% of the cost price:
\[ 140\% \text{ of CP} = SP_{new} \]
- This can be written as:
\[ \frac{140}{100} \times CP = SP_{new} \]
- Substitute the value of CP:
\[ SP_{new} = \frac{140}{100} \times 15 \]

5. **Calculate SP_{new}:**
- Now, calculate the new selling price:
\[ SP_{new} = \frac{140 \times 15}{100} = \frac{2100}{100} = 21 \]
- So, the new selling price (SP_{new}) for a 40% gain is Rs. 21.

6. **Calculate the Increase in Selling Price:**
- The increase in selling price is:
\[ Increase = SP_{new} - SP_{old} = 21 - 19.50 \]

7. **Calculate the Increase:**
- Now, calculate the increase:
\[ Increase = 21 - 19.50 = 1.50 \]
- Therefore, the increase in selling price is Rs. 1.50.

### Final Answer:
The increase in the selling price to gain 40% is Rs. 1.50.

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