the salary of an offiser is increased by 20% by what percentage should the new salary be reduced to restore the original salary?

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Let the Original Salary be 100x**:
- We assume the original salary of the officer is 100x. This makes calculations easier.

**Hint**: Assume a base value (like 100) to simplify percentage calculations.

2. **Calculate the New Salary After 20% Increase**:
- The salary is increased by 20%. To find the new salary, we calculate:
\[ \text{New Salary} = \text{Original Salary} + \text{Increase} \]
\[ \text{New Salary} = 100x + \left(\frac{20}{100} \times 100x\right) = 100x + 20x = 120x \]

**Hint**: To find a percentage increase, add the original amount to the calculated increase.

3. **Determine the Amount to Reduce the New Salary to Restore the Original Salary**:
- We need to find out how much percentage the new salary (120x) should be reduced to get back to the original salary (100x).

4. **Calculate the Difference Between New Salary and Original Salary**:
- The difference is:
\[ \text{Difference} = \text{New Salary} - \text{Original Salary} = 120x - 100x = 20x \]

**Hint**: The difference between the new and original salary is the amount that needs to be reduced.

5. **Use the Percentage Change Formula**:
- The formula for percentage change is:
\[ \text{Percentage Change} = \left(\frac{\text{Change}}{\text{Original Value}}\right) \times 100 \]
- Here, the change is 20x and the original value (the new salary) is 120x:
\[ \text{Percentage Reduction} = \left(\frac{20x}{120x}\right) \times 100 \]

**Hint**: Use the new salary as the base for calculating the percentage reduction.

6. **Simplify the Calculation**:
- Cancel out x:
\[ \text{Percentage Reduction} = \left(\frac{20}{120}\right) \times 100 = \frac{1}{6} \times 100 \]
- This simplifies to:
\[ \text{Percentage Reduction} = 16.67\% \]

**Hint**: When simplifying fractions, divide both the numerator and denominator by their greatest common divisor.

### Final Answer:
The new salary should be reduced by **16.67%** to restore the original salary.