A's salary was decreased by 50% and subsequently increased by 50%. How much per cent does he lose?

Options

A. A) 25%
B. B) 50%
C. C) 12 `1/2` %
D. D) No loss

Answer

To solve the problem of A's salary being decreased by 50% and then increased by 50%, we can follow these steps:

### Step-by-Step Solution:

1. **Initial Salary**: Let's assume A's initial salary is \(100\) (this makes calculations easier).

2. **Decrease by 50%**:
- A's salary is decreased by 50%.
- Calculation:
\[ \text{New Salary} = 100 - (50\% \text{ of } 100) = 100 - 50 = 50 \]
- So, after the decrease, A's salary is \(50\).

3. **Increase by 50%**:
- Now, A's salary of \(50\) is increased by 50%.
- Calculation:
\[ \text{New Salary} = 50 + (50\% \text{ of } 50) = 50 + 25 = 75 \]
- After the increase, A's salary is \(75\).

4. **Calculate the Loss**:
- To find out how much A has lost, we subtract the final salary from the initial salary.
- Calculation:
\[ \text{Loss} = 100 - 75 = 25 \]

5. **Calculate the Percentage Loss**:
- To find the percentage loss, we use the formula:
\[ \text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{Initial Salary}} \right) \times 100 \]
- Calculation:
\[ \text{Percentage Loss} = \left( \frac{25}{100} \right) \times 100 = 25\% \]

### Final Answer:
A loses \(25\%\) of his salary.

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