Income of Suman is first increased by 7% and then it is decreased by 7%. What is the change in her income?

Options

A. 0.49% (increase)
B. 0.39% (decrease)
C. 0.39% (increase)
D. 0.49% (decrease)

Answer

To solve the problem step by step, we will follow the instructions provided in the transcript and perform the necessary calculations.

### Step 1: Define Suman's Initial Income
Let Suman's initial income be \(100\) (this is a convenient choice to simplify percentage calculations).

### Step 2: Calculate the Income After the Increase
Suman's income is first increased by \(7\%\).

To find the increase:
\[ \text{Increase} = 7\% \text{ of } 100 = \frac{7}{100} \times 100 = 7 \]

Now, add this increase to the initial income:
\[ \text{New Income} = 100 + 7 = 107 \]

### Step 3: Calculate the Income After the Decrease
Next, Suman's income is decreased by \(7\%\) of the new income (\(107\)).

To find the decrease:
\[ \text{Decrease} = 7\% \text{ of } 107 = \frac{7}{100} \times 107 = 7.49 \]

Now, subtract this decrease from the new income:
\[ \text{Final Income} = 107 - 7.49 = 99.51 \]

### Step 4: Calculate the Change in Income
Now, we need to find the change in income compared to the original income:
\[ \text{Change in Income} = \text{Final Income} - \text{Initial Income} = 99.51 - 100 = -0.49 \]

### Step 5: Calculate the Percentage Change
To express this change as a percentage of the original income:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Income}}{\text{Initial Income}}\right) \times 100 = \left(\frac{-0.49}{100}\right) \times 100 = -0.49\% \]

### Conclusion
Suman's income has decreased by \(0.49\%\).

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