To attract more visitors, Zoo authority announces `20%` discount on every ticket which costs `29` paise. 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 will follow the logic presented in the video transcript while ensuring clarity in each step.

### Step 1: Understand the Initial Situation
Let’s assume the initial number of visitors to the zoo is 100.

**Hint:** Start by defining a base number for easier calculations.

### Step 2: Calculate Initial Revenue
The cost of each ticket is 29 paise (which is equivalent to Rs. 0.29). Therefore, the initial revenue from 100 visitors can be calculated as:
\[ \text{Initial Revenue} = \text{Number of Visitors} \times \text{Cost per Ticket} = 100 \times 0.29 = Rs. 29 \]

**Hint:** Revenue is calculated by multiplying the number of visitors by the ticket price.

### Step 3: Calculate the Discounted Ticket Price
The zoo authority announces a 20% discount on the ticket price. To find the new ticket price after the discount:
\[ \text{Discount} = 20\% \text{ of } 0.29 = \frac{20}{100} \times 0.29 = 0.058 \]
\[ \text{New Ticket Price} = 0.29 - 0.058 = 0.232 \text{ (or Rs. 0.232)} \]

**Hint:** Calculate the discount amount first, then subtract it from the original price to find the new price.

### Step 4: Calculate the Increase in Number of Visitors
The sale of tickets increases by 28%. Therefore, the new number of visitors can be calculated as:
\[ \text{New Number of Visitors} = \text{Initial Visitors} + \text{Increase} = 100 + (28\% \text{ of } 100) = 100 + 28 = 128 \]

**Hint:** To find the new number of visitors, add the percentage increase to the initial number.

### Step 5: Calculate New Revenue
Now, we can calculate the new revenue with the increased number of visitors:
\[ \text{New Revenue} = \text{New Number of Visitors} \times \text{New Ticket Price} = 128 \times 0.232 = Rs. 29.696 \]

**Hint:** Use the new number of visitors and the new ticket price to find the new revenue.

### Step 6: Calculate the Percentage Increase in Visitors
To find the percentage increase in the number of visitors:
\[ \text{Percentage Increase} = \left(\frac{\text{New Visitors} - \text{Initial Visitors}}{\text{Initial Visitors}}\right) \times 100 = \left(\frac{128 - 100}{100}\right) \times 100 = 28\% \]

**Hint:** The percentage increase is found by taking the difference in visitors, dividing by the original number, and multiplying by 100.

### Final Result
The percentage increase in the number of visitors is **28%**.