A person gave 20% of his income to his elder son, 30% of the re maining to the younger son and 10% of the balance, he donated to a trust. He is left with 10080. His income was:

Options

A. 50000
B. 40000
C. 30000
D. 20000

Answer

To find the total income of the person, we can break down the problem step by step.

### Step 1: Define the total income
Let the total income of the person be represented as \( I \).

### Step 2: Calculate the amount given to the elder son
The person gave 20% of his income to his elder son.
So, the amount given to the elder son is:
\[ \text{Amount to elder son} = 0.20 \times I = 0.2I \]

### Step 3: Calculate the remaining income after giving to the elder son
After giving 20% to the elder son, the remaining income is:
\[ \text{Remaining income} = I - 0.2I = 0.8I \]

### Step 4: Calculate the amount given to the younger son
The person then gave 30% of the remaining income to his younger son.
So, the amount given to the younger son is:
\[ \text{Amount to younger son} = 0.30 \times (0.8I) = 0.24I \]

### Step 5: Calculate the remaining income after giving to the younger son
After giving 30% to the younger son, the remaining income is:
\[ \text{Remaining income} = 0.8I - 0.24I = 0.56I \]

### Step 6: Calculate the amount donated to the trust
The person donated 10% of the remaining income to a trust.
So, the amount donated to the trust is:
\[ \text{Amount donated} = 0.10 \times (0.56I) = 0.056I \]

### Step 7: Calculate the remaining income after the donation
After donating 10% to the trust, the remaining income is:
\[ \text{Remaining income} = 0.56I - 0.056I = 0.504I \]

### Step 8: Set up the equation with the final amount left
We know that after all these transactions, the person is left with 10,080. Therefore, we can set up the equation:
\[ 0.504I = 10,080 \]

### Step 9: Solve for the total income \( I \)
To find \( I \), we divide both sides by 0.504:
\[ I = \frac{10,080}{0.504} \]
Calculating this gives:
\[ I = 20,000 \]

### Conclusion
The total income of the person is \( \boxed{20,000} \).

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