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

Options

A. 4% decreased
B. 4% increased
C. 8% decreased
D. neither decrease nor increase

Answer

To solve the problem step by step, let's denote the initial salary of the person as \( S \).

### Step 1: Calculate the salary after a 20% increase
When the salary is increased by 20%, the new salary can be calculated as follows:

\[ \text{New Salary} = S + 0.20S = 1.20S \]

### Step 2: Calculate the salary after a 20% decrease
Next, we need to decrease this new salary by 20%. The decrease is calculated on the new salary \( 1.20S \):

\[ \text{Decrease} = 0.20 \times 1.20S = 0.24S \]

Now, we subtract this decrease from the new salary:

\[ \text{Final Salary} = 1.20S - 0.24S = 0.96S \]

### Step 3: Determine the change in salary
Now we need to find the change in salary compared to the original salary \( S \):

\[ \text{Change in Salary} = \text{Final Salary} - \text{Original Salary} = 0.96S - S = -0.04S \]

### Step 4: Calculate the percentage change
To express this change as a percentage of the original salary, we calculate:

\[ \text{Percentage Change} = \left(\frac{-0.04S}{S}\right) \times 100\% = -4\% \]

Thus, the salary has decreased by 4%.

### Final Answer
The change in the person's salary is a decrease of **4%**.

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