Raju spends 40% of his salary on house rent, on remaining 10% spends on travel, on remains 16`2/3 `% spends on food and remaining is saved. If he saved Rs. 2250 what amount he spent food?

Options

A. Rs. 433`1/3`
B. Rs. 450
C. Rs. 530
D. None of these

Answer

To solve the problem step by step, we will break down Raju's spending based on the percentages given in the question.

### Step 1: Define Raju's Salary
Let Raju's total salary be \( S \).

### Step 2: Calculate House Rent
Raju spends 40% of his salary on house rent:
\[ \text{House Rent} = 0.40S \]

### Step 3: Calculate Remaining Salary After House Rent
The remaining salary after paying the house rent is:
\[ \text{Remaining Salary} = S - 0.40S = 0.60S \]

### Step 4: Calculate Travel Expenses
Raju spends 10% of the remaining salary on travel:
\[ \text{Travel Expenses} = 0.10 \times 0.60S = 0.06S \]

### Step 5: Calculate Remaining Salary After Travel
The remaining salary after travel expenses is:
\[ \text{Remaining Salary After Travel} = 0.60S - 0.06S = 0.54S \]

### Step 6: Calculate Food Expenses
Raju spends \( 16 \frac{2}{3} \% \) (which is \( \frac{50}{3} \% \) or \( \frac{1}{6} \)) of the remaining salary on food:
\[ \text{Food Expenses} = \frac{50}{3} \% \text{ of } 0.54S = \frac{50}{300} \times 0.54S = \frac{1}{6} \times 0.54S = 0.09S \]

### Step 7: Calculate Remaining Salary After Food
The remaining salary after food expenses is:
\[ \text{Remaining Salary After Food} = 0.54S - 0.09S = 0.45S \]

### Step 8: Set Up Equation for Savings
According to the problem, Raju saves Rs. 2250:
\[ 0.45S = 2250 \]

### Step 9: Calculate Raju's Salary
To find \( S \):
\[ S = \frac{2250}{0.45} = 5000 \]

### Step 10: Calculate Food Expenses
Now, we can find out how much Raju spent on food:
\[ \text{Food Expenses} = 0.09S = 0.09 \times 5000 = 450 \]

Thus, the amount Raju spent on food is **Rs. 450**.

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