Amit donated `20%` of his income to a school and deposited `20%` of the remainder in his bank. If he is having `Rs. 12800` now, then what is the income (in Rs) of Amit ?

Options

A. `18000`
B. `20000`
C. `24000`
D. `32000`

Answer

To find Amit's income based on the information provided, we can follow these steps:

1. **Let Amit's total income be represented as \( x \)**.
- We can express his income in terms of a variable for easier calculations.

2. **Calculate the amount donated to the school**:
- Amit donated \( 20\% \) of his income, which can be calculated as:
\[ \text{Donation} = 0.20 \times x = 0.2x \]

3. **Determine the remaining income after the donation**:
- After donating, the remaining income is:
\[ \text{Remaining Income} = x - 0.2x = 0.8x \]

4. **Calculate the amount deposited in the bank**:
- Amit deposited \( 20\% \) of the remaining income into his bank:
\[ \text{Deposit} = 0.20 \times (0.8x) = 0.16x \]

5. **Find the remaining amount after the deposit**:
- The amount left after the deposit is:
\[ \text{Remaining Amount} = 0.8x - 0.16x = 0.64x \]

6. **Set up the equation based on the remaining amount**:
- We know that the remaining amount is \( Rs. 12800 \):
\[ 0.64x = 12800 \]

7. **Solve for \( x \)**:
- To find \( x \), divide both sides of the equation by \( 0.64 \):
\[ x = \frac{12800}{0.64} = 20000 \]

8. **Conclusion**:
- Therefore, Amit's total income is \( Rs. 20000 \).