Every month ,Kritika spends `30%` of her income on house rent and `60%` of the rest on household expenditure .If she saves Rs. 6300 per month ,what is her total monthly income ?

Options

A. Rs. 22,000
B. Rs. 20,500
C. Rs. 22,500
D. Rs. 25,000

Answer

To solve the problem step by step, we will denote Kritika's total monthly income as \( I \).

### Step 1: Calculate the amount spent on house rent
Kritika spends 30% of her income on house rent. Therefore, the amount spent on house rent is:
\[ \text{House Rent} = 0.30 \times I \]

### Step 2: Calculate the remaining income after house rent
After paying the house rent, the remaining income is:
\[ \text{Remaining Income} = I - \text{House Rent} = I - 0.30I = 0.70I \]

### Step 3: Calculate the amount spent on household expenditure
Kritika spends 60% of her remaining income on household expenditure. Therefore, the amount spent on household expenditure is:
\[ \text{Household Expenditure} = 0.60 \times \text{Remaining Income} = 0.60 \times 0.70I = 0.42I \]

### Step 4: Calculate total expenditure
Now, we can calculate her total expenditure, which is the sum of house rent and household expenditure:
\[ \text{Total Expenditure} = \text{House Rent} + \text{Household Expenditure} = 0.30I + 0.42I = 0.72I \]

### Step 5: Calculate savings
Kritika saves Rs. 6300 per month. Therefore, we can express her savings as:
\[ \text{Savings} = \text{Income} - \text{Total Expenditure} = I - 0.72I = 0.28I \]

### Step 6: Set up the equation for savings
Since we know that her savings amount to Rs. 6300, we can set up the equation:
\[ 0.28I = 6300 \]

### Step 7: Solve for total monthly income
To find \( I \), we can rearrange the equation:
\[ I = \frac{6300}{0.28} \]

Calculating this gives:
\[ I = \frac{6300 \times 100}{28} = \frac{630000}{28} = 22500 \]

### Final Result
Kritika's total monthly income is Rs. 22,500.

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