Rajiv's salary was reduced by `20%` in a year and subsequently increased by `30%` the following year. What is the overall percentage change over the original salary?

Options

A. a. `24%`
B. b. `4%`
C. c. `10%`
D. d. `6%`

Answer

To find the overall percentage change in Rajiv's salary after a reduction of 20% followed by an increase of 30%, we can follow these steps:

### Step 1: Assume the Original Salary
Let's assume Rajiv's original salary is \( S = 100 \).

### Step 2: Calculate the Salary After the 20% Reduction
A reduction of 20% means Rajiv will receive 80% of his original salary.

\[ \text{New Salary after Reduction} = S - (20\% \text{ of } S) = 100 - (0.20 \times 100) = 100 - 20 = 80 \]

### Step 3: Calculate the Salary After the 30% Increase
Now, we need to calculate the new salary after a 30% increase on the reduced salary of 80.

\[ \text{Increase} = 30\% \text{ of } 80 = 0.30 \times 80 = 24 \]
\[ \text{New Salary after Increase} = 80 + 24 = 104 \]

### Step 4: Calculate the Overall Change in Salary
Now, we find the overall change in salary from the original salary of 100 to the new salary of 104.

\[ \text{Change in Salary} = 104 - 100 = 4 \]

### Step 5: Calculate the Percentage Change
To find the percentage change, we use the formula:

\[ \text{Percentage Change} = \left( \frac{\text{Change in Salary}}{\text{Original Salary}} \right) \times 100 \]

Substituting the values we have:

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

### Conclusion
The overall percentage change in Rajiv's salary is **4%**.

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