After deducting `12%` from a certain sum and then deducting `25%` from the remainder, `2508` is left, then what is the initial sum ?

Options

A. `3500`
B. `3450`
C. `3970`
D. `3800`

Answer

To find the initial sum after deducting 12% and then 25% from it, we can follow these steps:

### Step-by-Step Solution:

1. **Let the initial sum be \( x \)**.
- We start by defining the initial amount as \( x \).

2. **Calculate the amount after deducting 12%**:
- Deducting 12% from \( x \) means we are left with \( 88\% \) of \( x \).
- This can be calculated as:
\[ \text{Amount after 12% deduction} = x - 0.12x = 0.88x \]

3. **Calculate the amount after deducting 25% from the remainder**:
- Now, we need to deduct 25% from \( 0.88x \). This means we are left with \( 75\% \) of \( 0.88x \).
- This can be calculated as:
\[ \text{Amount after 25% deduction} = 0.88x - 0.25 \times 0.88x = 0.75 \times 0.88x = 0.66x \]

4. **Set the final amount equal to 2508**:
- According to the problem, after these deductions, we are left with \( 2508 \):
\[ 0.66x = 2508 \]

5. **Solve for \( x \)**:
- To find \( x \), we divide both sides of the equation by \( 0.66 \):
\[ x = \frac{2508}{0.66} \]
- Performing the division:
\[ x = 3800 \]

### Final Answer:
The initial sum is \( 3800 \).

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