after spending 80% of his income and giving 10% of the remainder in a charity a man has ₹ 46260 left white him find his income

Answer

To solve the problem step by step, we can follow these calculations:

1. **Define the Variables**:
Let the man's total income be represented as \( X \).

2. **Calculate the Amount Spent**:
The man spends 80% of his income. Therefore, the amount spent is:
\[ \text{Amount spent} = 0.80X \]

3. **Calculate the Remaining Amount**:
After spending 80% of his income, the remaining amount is:
\[ \text{Remaining amount} = X - 0.80X = 0.20X \]

4. **Calculate the Charity Amount**:
He gives 10% of the remaining amount to charity. The amount given to charity is:
\[ \text{Charity amount} = 0.10 \times (0.20X) = 0.02X \]

5. **Calculate the Amount Left After Charity**:
After giving to charity, the amount left with him is:
\[ \text{Amount left} = \text{Remaining amount} - \text{Charity amount} = 0.20X - 0.02X = 0.18X \]

6. **Set Up the Equation**:
According to the problem, the amount left with him is ₹ 46,260. Therefore, we can set up the equation:
\[ 0.18X = 46260 \]

7. **Solve for \( X \)**:
To find \( X \), divide both sides of the equation by 0.18:
\[ X = \frac{46260}{0.18} \]
\[ X = 257000 \]

8. **Conclusion**:
The man's total income is ₹ 257,000.