To attract more visitors Zoo authority announces 20% discount on every ticket which costs 25 paisa. For this reason, sale of ticket increases by 28%. Find the percentage of increase in the number of visitors.

Options

A. 40%
B. 50%
C. 60%
D. No change

Answer

To solve the problem step by step, we need to analyze the information provided and calculate the required percentage increase in the number of visitors to the zoo after a discount is applied to the ticket price.

### Step 1: Determine the original ticket price and the discounted price.
- The original ticket price is given as 25 paisa.
- A 20% discount on the ticket means the new price will be:
\[ \text{Discount} = 20\% \text{ of } 25 \text{ paisa} = \frac{20}{100} \times 25 = 5 \text{ paisa} \]
- Therefore, the new ticket price after the discount is:
\[ \text{New Price} = 25 \text{ paisa} - 5 \text{ paisa} = 20 \text{ paisa} \]

### Step 2: Calculate the increase in ticket sales.
- The problem states that the sale of tickets increases by 28%.
- If we assume the original number of tickets sold is 100 (for simplicity), then the increase in sales can be calculated as:
\[ \text{Increase in Sales} = 28\% \text{ of } 100 = 28 \text{ tickets} \]
- Therefore, the new number of tickets sold becomes:
\[ \text{New Sales} = 100 + 28 = 128 \text{ tickets} \]

### Step 3: Relate the increase in sales to the increase in visitors.
- The original number of visitors can be assumed to be proportional to the original number of tickets sold. If we denote the original number of visitors as \( V \), we can set up a ratio based on the ticket prices.
- The ratio of original sales to new sales is:
\[ \frac{100}{128} = \frac{25}{32} \]
- The ratio of the original price to the new price is:
\[ \frac{25 \text{ paisa}}{20 \text{ paisa}} = \frac{5}{4} \]
- Setting these two ratios equal gives us:
\[ \frac{25}{32} = \frac{5}{4} \cdot \frac{V}{V'} \]
where \( V' \) is the new number of visitors.

### Step 4: Solve for the new number of visitors.
- Rearranging gives:
\[ \frac{V'}{V} = \frac{32}{25} \cdot \frac{4}{5} = \frac{32 \cdot 4}{25 \cdot 5} = \frac{128}{125} \]
- This means the new number of visitors \( V' \) is:
\[ V' = V \cdot \frac{128}{125} \]

### Step 5: Calculate the percentage increase in the number of visitors.
- The increase in the number of visitors is:
\[ \text{Increase} = V' - V = V \cdot \frac{128}{125} - V = V \left(\frac{128}{125} - 1\right) = V \cdot \frac{3}{125} \]
- The percentage increase is then:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase}}{V}\right) \cdot 100 = \left(\frac{3}{125}\right) \cdot 100 = 2.4\% \]

### Conclusion
The percentage increase in the number of visitors is 2.4%.