A man donated `6%` of his income to a charity and deposited `20%` of the rest in a bank. If he is left with Rs. 14,100, then his income is `"________".`

Options

A. Rs. 18000
B. Rs. 18250
C. Rs. 18500
D. Rs. 18750

Explanation

To solve the problem step by step, we will denote the man's income as \( x \).

### Step 1: Calculate the amount donated to charity
The man donated 6% of his income to charity. Therefore, the amount donated can be calculated as:
\[ \text{Amount donated} = \frac{6}{100} \times x = 0.06x \]

### Step 2: Calculate the remaining amount after the donation
After donating to charity, the remaining amount is:
\[ \text{Remaining amount after charity} = x - 0.06x = 0.94x \]

### Step 3: Calculate the amount deposited in the bank
The man then deposited 20% of the remaining amount in the bank. The amount deposited in the bank is:
\[ \text{Amount deposited} = \frac{20}{100} \times (0.94x) = 0.2 \times 0.94x = 0.188x \]

### Step 4: Calculate the remaining amount after the bank deposit
After depositing in the bank, the remaining amount is:
\[ \text{Remaining amount after deposit} = 0.94x - 0.188x = 0.752x \]

### Step 5: Set up the equation based on the remaining amount
According to the problem, the man is left with Rs. 14,100. Therefore, we can set up the equation:
\[ 0.752x = 14,100 \]

### Step 6: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 0.752:
\[ x = \frac{14,100}{0.752} \]

Calculating this gives:
\[ x \approx 18,750 \]

### Conclusion
Thus, the man's income is Rs. 18,750.

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