Neeraj's earning was decreased by 60% and after that subsequently increased by 60%. Find the final loss % on his earnings?

A. 12%

B. 36%

C. 4%

D. 5%

Options

A. B
B. C
C. D
D. A

Answer

To find the final loss percentage on Neeraj's earnings after a decrease and subsequent increase, we can follow these steps:

### Step-by-Step Solution:

1. **Initial Earnings**:
Let's assume Neeraj's initial earnings are \( 100x \).

2. **Decrease in Earnings**:
Neeraj's earnings decreased by 60%.
- The remaining earnings after the decrease = \( 100x - 60\% \text{ of } 100x \)
- This can be calculated as:
\[ \text{Remaining Earnings} = 100x \times (1 - 0.60) = 100x \times 0.40 = 40x \]

3. **Increase in Earnings**:
After the decrease, Neeraj's earnings are increased by 60%.
- The new earnings after the increase = \( 40x + 60\% \text{ of } 40x \)
- This can be calculated as:
\[ \text{New Earnings} = 40x \times (1 + 0.60) = 40x \times 1.60 = 64x \]

4. **Calculating the Loss**:
Now, we need to find the loss in earnings.
- The loss = Initial Earnings - New Earnings
- This can be calculated as:
\[ \text{Loss} = 100x - 64x = 36x \]

5. **Calculating the Loss Percentage**:
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Initial Earnings}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{36x}{100x} \right) \times 100 = 36\% \]

### Final Answer:
The final loss percentage on Neeraj's earnings is **36%**.