The salary of a worker is first increased by 5% and then it is decreased by 5%. What is the change in his salary?

Answer

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

### Step 1: Define the Initial Salary
Let's assume the initial salary of the worker is \( S = 100 \).

### Step 2: Calculate the Salary After the 5% Increase
To find the new salary after a 5% increase, we calculate:
\[ \text{Increased Salary} = S + (5\% \text{ of } S) = S + \frac{5}{100} \times S \]
Substituting \( S = 100 \):
\[ \text{Increased Salary} = 100 + \frac{5}{100} \times 100 = 100 + 5 = 105 \]

### Step 3: Calculate the Salary After the 5% Decrease
Next, we calculate the salary after a 5% decrease from the increased salary of 105:
\[ \text{Decreased Salary} = \text{Increased Salary} - (5\% \text{ of Increased Salary}) = 105 - \frac{5}{100} \times 105 \]
Calculating \( 5\% \text{ of } 105 \):
\[ \frac{5}{100} \times 105 = 5.25 \]
Now, substituting back:
\[ \text{Decreased Salary} = 105 - 5.25 = 99.75 \]

### Step 4: Calculate the Change in Salary
Now, we find the change in salary by subtracting the initial salary from the decreased salary:
\[ \text{Change} = \text{Decreased Salary} - \text{Initial Salary} = 99.75 - 100 = -0.25 \]

### Step 5: Calculate the Percentage Change
Finally, we calculate the percentage change in salary:
\[ \text{Percentage Change} = \left( \frac{\text{Change}}{\text{Initial Salary}} \right) \times 100 = \left( \frac{-0.25}{100} \right) \times 100 = -0.25\% \]

### Conclusion
The change in the worker's salary after a 5% increase followed by a 5% decrease is a decrease of \( 0.25\% \).

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