Rohit spends `5%` of his income on insurance and `2(1)/(2)%` of the remaining paying as tax. Now he is left with `Rs.420` more than `90%` of his income. Find his income.

Options

A. Rs. `16,000`
B. Rs. `18,000`
C. Rs. `24,000`
D. Rs. `19,000`

Answer

To find Rohit's income based on the given problem, let's break it down step by step.

### Step 1: Define Rohit's total income
Let Rohit's total income be represented as \( I \).

### Step 2: Calculate the amount spent on insurance
Rohit spends \( 5\% \) of his income on insurance. Therefore, the amount spent on insurance is:
\[ \text{Insurance} = \frac{5}{100} \times I = 0.05I \]

### Step 3: Calculate the remaining income after insurance
After spending on insurance, the remaining income is:
\[ \text{Remaining Income} = I - 0.05I = 0.95I \]

### Step 4: Calculate the amount spent on tax
Rohit spends \( 2.5\% \) (which is \( 2\frac{1}{2}\% \)) of the remaining income on tax. Therefore, the amount spent on tax is:
\[ \text{Tax} = \frac{2.5}{100} \times 0.95I = 0.025 \times 0.95I = 0.02375I \]

### Step 5: Calculate the remaining income after tax
After spending on tax, the remaining income is:
\[ \text{Remaining Income after Tax} = 0.95I - 0.02375I = 0.92625I \]

### Step 6: Set up the equation based on the given condition
According to the problem, Rohit is left with \( Rs.420 \) more than \( 90\% \) of his income. Thus, we can express this as:
\[ 0.92625I = 0.90I + 420 \]

### Step 7: Simplify the equation
Now, let's simplify the equation:
\[ 0.92625I - 0.90I = 420 \]
\[ 0.02625I = 420 \]

### Step 8: Solve for \( I \)
To find \( I \), divide both sides by \( 0.02625 \):
\[ I = \frac{420}{0.02625} \]
Calculating this gives:
\[ I = 16000 \]

### Conclusion
Thus, Rohit's total income is \( \text{Rs.} 16000 \).

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