The price of an article is reduced by 25% but the daily sale of the article is increased by 30%. The net effect on the daily sale receipts is

Options

A. `2 (1)/(2)` % decrease
B. `2 (1)/(2)` % increase
C. 2% decrease
D. 2% increase

Answer

To solve the problem step by step, we will follow the calculations as described in the video transcript.

### Step-by-Step Solution:

1. **Assume the Initial Price and Sales:**
- Let the initial price of the article be \( P = 100 \) rupees.
- Let the initial number of articles sold be \( Q = 100 \).
- Therefore, the initial total sales (receipts) \( SI \) can be calculated as:
\[ SI = P \times Q = 100 \times 100 = 10,000 \text{ rupees} \]

2. **Calculate the Reduced Price:**
- The price is reduced by 25%. Therefore, the reduced price \( P' \) is:
\[ P' = P - (0.25 \times P) = 100 - (0.25 \times 100) = 100 - 25 = 75 \text{ rupees} \]

3. **Calculate the Increased Quantity Sold:**
- The daily sale of the article increases by 30%. Therefore, the new quantity sold \( Q' \) is:
\[ Q' = Q + (0.30 \times Q) = 100 + (0.30 \times 100) = 100 + 30 = 130 \]

4. **Calculate the New Total Sales:**
- Now, we calculate the new total sales \( SF \) with the reduced price and increased quantity:
\[ SF = P' \times Q' = 75 \times 130 \]
- Performing the multiplication:
\[ SF = 75 \times 130 = 9750 \text{ rupees} \]

5. **Calculate the Change in Sales:**
- Now, we find the change in sales receipts:
\[ \text{Change} = SF - SI = 9750 - 10000 = -250 \text{ rupees} \]

6. **Calculate the Percentage Decrease:**
- To find the percentage decrease in sales receipts, we use the formula:
\[ \text{Percentage Decrease} = \left( \frac{SF - SI}{SI} \right) \times 100 = \left( \frac{-250}{10000} \right) \times 100 \]
- Simplifying this gives:
\[ \text{Percentage Decrease} = -2.5\% \]

### Final Answer:
The net effect on the daily sale receipts is a decrease of **2.5%**.