Chinu donated `10%` of his income to an orphanage and deposited `20%` of the remaining in the bank if he has now `Rs7200` left what is his income ?

Options

A. Rs. `12,000`
B. Rs. `14,000`
C. Rs. `10,000`
D. Rs. `8,000`

Answer

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

### Step 1: Calculate the amount donated
Chinu donated \( 10\% \) of his income to an orphanage. Therefore, the amount he donated is:
\[ \text{Donation} = 10\% \text{ of } x = \frac{10}{100} \cdot x = 0.1x \]

### Step 2: Calculate the remaining income after donation
After donating, the remaining income is:
\[ \text{Remaining Income} = x - \text{Donation} = x - 0.1x = 0.9x \]

### Step 3: Calculate the amount deposited in the bank
Chinu then deposited \( 20\% \) of the remaining income in the bank. The amount deposited is:
\[ \text{Deposit} = 20\% \text{ of } (0.9x) = \frac{20}{100} \cdot (0.9x) = 0.18x \]

### Step 4: Calculate the remaining income after the deposit
The remaining income after the deposit is:
\[ \text{Final Remaining Income} = \text{Remaining Income} - \text{Deposit} = 0.9x - 0.18x = 0.72x \]

### Step 5: Set up the equation based on the final amount left
According to the problem, Chinu has Rs 7200 left after these transactions:
\[ 0.72x = 7200 \]

### Step 6: Solve for \( x \)
To find Chinu's total income \( x \), we can rearrange the equation:
\[ x = \frac{7200}{0.72} \]
Calculating this gives:
\[ x = 10000 \]

### Conclusion
Chinu's total income is Rs 10,000.

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