Salary of a person is first increased by 20%, then it is decreased by 20%. Percentage change in his salary is:

Options

A. 4% decreased
B. 4% Increased
C. 8% decreased
D. 20% Increased

Answer

To solve the problem of finding the percentage change in a person's salary after it is first increased by 20% and then decreased by 20%, we can follow these steps:

### Step 1: Understand the initial salary
Let's assume the initial salary of the person is \( S \).

### Step 2: Calculate the salary after the 20% increase
When the salary is increased by 20%, the new salary can be calculated as:
\[ \text{New Salary after increase} = S + 0.20S = 1.20S \]

### Step 3: Calculate the salary after the 20% decrease
Next, we need to decrease this new salary by 20%. The decrease is calculated on the new salary:
\[ \text{Decrease} = 0.20 \times (1.20S) = 0.24S \]
So, the salary after the decrease will be:
\[ \text{Final Salary} = 1.20S - 0.24S = 0.96S \]

### Step 4: Calculate the percentage change in salary
The percentage change in salary can be calculated using the formula:
\[ \text{Percentage Change} = \left(\frac{\text{Final Salary} - \text{Initial Salary}}{\text{Initial Salary}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Change} = \left(\frac{0.96S - S}{S}\right) \times 100 = \left(\frac{-0.04S}{S}\right) \times 100 = -4\% \]

### Conclusion
Thus, the percentage change in the person's salary is a decrease of 4%.

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