A number is increaesd bt 20% given 30. the number is

Options

A. 150
B. 6
C. 25
D. 60

Answer

To find the original number that, when increased by 20%, equals 30, we can follow these steps:

### Step-by-Step Solution:

1. **Let the original number be \( X \)**.
- We are trying to find this number.

2. **Calculate 20% of \( X \)**.
- The formula for percentage is:
\[ \text{Percentage} = \frac{\text{Value}}{100} \times \text{Total} \]
- Therefore, 20% of \( X \) can be calculated as:
\[ \frac{20}{100} \times X = \frac{20X}{100} = \frac{X}{5} \]

3. **Set up the equation for the increased number**.
- When we increase \( X \) by 20%, the new value becomes:
\[ X + \frac{X}{5} \]
- To combine these, we need a common denominator:
\[ X + \frac{X}{5} = \frac{5X}{5} + \frac{X}{5} = \frac{6X}{5} \]

4. **Set the equation equal to 30**.
- According to the problem, this increased number equals 30:
\[ \frac{6X}{5} = 30 \]

5. **Solve for \( X \)**.
- To eliminate the fraction, multiply both sides by 5:
\[ 6X = 30 \times 5 \]
\[ 6X = 150 \]
- Now, divide both sides by 6:
\[ X = \frac{150}{6} = 25 \]

6. **Conclusion**.
- The original number is \( 25 \).

### Final Answer:
The number is **25**.