Naresh's monthly income is reduced by 15%. By what percentage his monthly income must be increased so that it is again equal to his original monthly income?

Options

A. 17.6%
B. 14.6%
C. 15.6%
D. 16.6%

Answer

To solve the problem step by step, we can follow these calculations:

1. **Let the original monthly income be 100.**
- This is a convenient assumption that simplifies calculations.

2. **Calculate the reduced income after a 15% decrease.**
- A 15% decrease from 100 is calculated as:
\[ \text{Reduced Income} = 100 - (15\% \text{ of } 100) = 100 - 15 = 85 \]

3. **Determine how much income needs to be added to return to the original amount.**
- To find out how much needs to be added to 85 to get back to 100:
\[ \text{Amount to be added} = 100 - 85 = 15 \]

4. **Calculate the percentage increase required.**
- The percentage increase is calculated based on the reduced income (85):
\[ \text{Percentage Increase} = \left(\frac{\text{Amount to be added}}{\text{Reduced Income}}\right) \times 100 = \left(\frac{15}{85}\right) \times 100 \]
- Performing the division:
\[ \frac{15}{85} \approx 0.1765 \]
- Now multiply by 100 to convert to percentage:
\[ 0.1765 \times 100 \approx 17.65\% \]

5. **Conclusion:**
- Therefore, Naresh's monthly income must be increased by approximately **17.65%** to return to his original income.