out of her total monthly income Mrs Saxena spend 30% on house rent and 60% of the rest on household expenses. if she saved 6300 per mouth, what is her total monthly income

Answer

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

### Step 1: Calculate the amount spent on house rent
Mrs. Saxena spends 30% of her total income on house rent. Therefore, the amount spent on house rent is:
\[ \text{House Rent} = 30\% \text{ of } x = \frac{30}{100} \times x = 0.3x \]

### Step 2: Calculate the remaining income after house rent
To find out how much money is left after paying the house rent, we subtract the house rent from her total income:
\[ \text{Remaining Income} = x - \text{House Rent} = x - 0.3x = 0.7x \]

### Step 3: Calculate the amount spent on household expenses
Mrs. Saxena spends 60% of the remaining income on household expenses. Therefore, the amount spent on household expenses is:
\[ \text{Household Expenses} = 60\% \text{ of Remaining Income} = 60\% \text{ of } 0.7x = \frac{60}{100} \times 0.7x = 0.42x \]

### Step 4: Calculate the amount saved
To find out how much Mrs. Saxena saves, we subtract both the house rent and the household expenses from her total income:
\[ \text{Savings} = x - (\text{House Rent} + \text{Household Expenses}) = x - (0.3x + 0.42x) \]
\[ \text{Savings} = x - 0.72x = 0.28x \]

### Step 5: Set up the equation based on savings
According to the problem, Mrs. Saxena saves 6300 per month. Therefore, we can set up the equation:
\[ 0.28x = 6300 \]

### Step 6: Solve for \( x \)
To find the total monthly income \( x \), we divide both sides of the equation by 0.28:
\[ x = \frac{6300}{0.28} \]
\[ x = 22500 \]

### Conclusion
Mrs. Saxena's total monthly income is \( 22500 \).

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