Amit donated 20% of his income to a school and deposit ed 20% of the remainder in his bank. If he has Rs. 12800 now, 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:

### Step 1: Define Amit's Income
Let Amit's total income be represented as \( I \).

### Step 2: Calculate the Donation
Amit donated 20% of his income to the school. Therefore, the amount donated is:
\[ \text{Donation} = 0.20 \times I = \frac{I}{5} \]

### Step 3: Calculate the Remainder After Donation
After donating, the remaining income is:
\[ \text{Remaining Income} = I - \text{Donation} = I - \frac{I}{5} = \frac{5I}{5} - \frac{I}{5} = \frac{4I}{5} \]

### Step 4: Calculate the Bank Deposit
Amit then deposited 20% of the remaining income in the bank. The amount deposited in the bank is:
\[ \text{Bank Deposit} = 0.20 \times \text{Remaining Income} = 0.20 \times \frac{4I}{5} = \frac{4I}{25} \]

### Step 5: Calculate the Amount Left After Bank Deposit
The amount left after the bank deposit is:
\[ \text{Amount Left} = \text{Remaining Income} - \text{Bank Deposit} = \frac{4I}{5} - \frac{4I}{25} \]

To perform this subtraction, we need a common denominator. The common denominator for 5 and 25 is 25:
\[ \frac{4I}{5} = \frac{20I}{25} \]
Now we can subtract:
\[ \text{Amount Left} = \frac{20I}{25} - \frac{4I}{25} = \frac{16I}{25} \]

### Step 6: Set Up the Equation
According to the problem, the amount left after all donations and deposits is Rs. 12800. Therefore, we can set up the equation:
\[ \frac{16I}{25} = 12800 \]

### Step 7: Solve for Amit's Income
To find \( I \), we can multiply both sides of the equation by 25:
\[ 16I = 12800 \times 25 \]
Calculating the right side:
\[ 12800 \times 25 = 320000 \]
Now, divide both sides by 16:
\[ I = \frac{320000}{16} = 20000 \]

### Conclusion
Amit's income is Rs. 20000.

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