Raja gave `20%` of his income to his daughter, `40% `of the remaining to his first son, `30%` of the remaining to his second son finally the remaining Rs 12600 was donated to a charitable trust. Find Raja's income.

Answer

To solve the problem step by step, let's denote Raja's total income as \( x \).

### Step 1: Calculate the amount given to the daughter
Raja gives 20% of his income to his daughter.
\[ \text{Amount given to daughter} = 20\% \text{ of } x = \frac{20}{100} \times x = 0.2x \]

### Step 2: Calculate the remaining income after giving to the daughter
After giving 20% to his daughter, the remaining income is:
\[ \text{Remaining income} = x - 0.2x = 0.8x \]

### Step 3: Calculate the amount given to the first son
Raja gives 40% of the remaining income to his first son.
\[ \text{Amount given to first son} = 40\% \text{ of } 0.8x = \frac{40}{100} \times 0.8x = 0.32x \]

### Step 4: Calculate the remaining income after giving to the first son
The remaining income after giving to the first son is:
\[ \text{Remaining income} = 0.8x - 0.32x = 0.48x \]

### Step 5: Calculate the amount given to the second son
Raja gives 30% of the remaining income to his second son.
\[ \text{Amount given to second son} = 30\% \text{ of } 0.48x = \frac{30}{100} \times 0.48x = 0.144x \]

### Step 6: Calculate the remaining income after giving to the second son
The remaining income after giving to the second son is:
\[ \text{Remaining income} = 0.48x - 0.144x = 0.336x \]

### Step 7: Set the remaining amount equal to Rs 12,600
According to the problem, the remaining amount is Rs 12,600. Therefore, we can set up the equation:
\[ 0.336x = 12600 \]

### Step 8: Solve for \( x \)
To find Raja's total income, we divide both sides by 0.336:
\[ x = \frac{12600}{0.336} \approx 37500 \]

### Conclusion
Raja's total income is Rs 37,500.

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