In the Regional Science Centre, Lucknow the rate of ticket is increased by `50%` to increase the revenue, but simultaneously `20%` of the visitors decreased. What is percentage change in the revenue of Regional Science Centre. If it is known that the centre collects the revenue only from the visitors and it has no other financial supports:

Options

A. `+20%`
B. `-25%`
C. `+30%`
D. can't be determined

Answer

To find the percentage change in revenue for the Regional Science Centre after the increase in ticket prices and the decrease in visitors, we can follow these steps:

### Step-by-Step Solution:

1. **Define Initial Conditions**:
- Let the initial ticket price be \( P \).
- Let the initial number of visitors be \( V \).
- Therefore, the initial revenue \( R \) can be calculated as:
\[ R = P \times V \]

2. **Calculate New Ticket Price**:
- The ticket price is increased by \( 50\% \).
- New ticket price \( P' \) is given by:
\[ P' = P + 0.5P = 1.5P \]

3. **Calculate New Number of Visitors**:
- The number of visitors decreases by \( 20\% \).
- New number of visitors \( V' \) is given by:
\[ V' = V - 0.2V = 0.8V \]

4. **Calculate New Revenue**:
- The new revenue \( R' \) can be calculated as:
\[ R' = P' \times V' = (1.5P) \times (0.8V) = 1.2PV \]

5. **Calculate Percentage Change in Revenue**:
- The percentage change in revenue can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{R' - R}{R} \right) \times 100 \]
- Substituting the values of \( R' \) and \( R \):
\[ \text{Percentage Change} = \left( \frac{1.2PV - PV}{PV} \right) \times 100 = \left( \frac{0.2PV}{PV} \right) \times 100 = 20\% \]

### Final Answer:
The percentage change in the revenue of the Regional Science Centre is **20%**.