Out of his total income, Mr. Kapur spends 20% on house rent and 70% of the rest on house-hold expenses. If he saves 1,800, what is his total income (in rupees)?

Options

A. A) 7800
B. B) 7000
C. C) 8000
D. D) 7500

Answer

To solve the problem step by step, we will break down Mr. Kapur's income, expenses, and savings systematically.

### Step 1: Define Mr. Kapur's Total Income
Let Mr. Kapur's total income be represented as \( I \).

### Step 2: Calculate House Rent
Mr. Kapur spends 20% of his total income on house rent. Therefore, the amount spent on house rent is:
\[ \text{House Rent} = 0.20 \times I \]

### Step 3: Calculate Remaining Income After House Rent
After paying for house rent, the remaining income is:
\[ \text{Remaining Income} = I - \text{House Rent} = I - 0.20I = 0.80I \]

### Step 4: Calculate Household Expenses
Mr. Kapur spends 70% of the remaining income on household expenses. Therefore, the amount spent on household expenses is:
\[ \text{Household Expenses} = 0.70 \times \text{Remaining Income} = 0.70 \times 0.80I = 0.56I \]

### Step 5: Calculate Savings
The amount saved by Mr. Kapur is given as 1,800 rupees. The savings can be calculated as:
\[ \text{Savings} = \text{Remaining Income} - \text{Household Expenses} \]
Substituting the values we have:
\[ 1800 = 0.80I - 0.56I \]
\[ 1800 = 0.24I \]

### Step 6: Solve for Total Income
To find the total income \( I \), we rearrange the equation:
\[ I = \frac{1800}{0.24} \]
Calculating this gives:
\[ I = 7500 \]

### Conclusion
Mr. Kapur's total income is **7,500 rupees**.

---