A family consumes Rice, Daal and Wheat. The ratio of its expenditure is 12 : 17 : 3. If the price of those commodities increases by `20%, 30% and 50%` respectively. By how much expenditure will be increased of that family.

Answer

To solve the problem, we need to calculate the increase in expenditure for the family after the price hikes of rice, daal, and wheat. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Ratios
The expenditure ratio for rice, daal, and wheat is given as:
- Rice: 12 parts
- Daal: 17 parts
- Wheat: 3 parts

### Step 2: Calculate the Total Original Expenditure
The total original expenditure can be calculated by summing the parts of the ratio:
\[ \text{Total Original Expenditure} = 12 + 17 + 3 = 32 \text{ parts} \]

### Step 3: Determine the Price Increase
The prices of the commodities increase as follows:
- Rice: Increases by 20%
- Daal: Increases by 30%
- Wheat: Increases by 50%

### Step 4: Calculate the New Expenditure for Each Commodity
We will calculate the new expenditure for each commodity by applying the respective price increases to their original expenditure ratios.

**For Rice:**
- Original expenditure = 12 parts
- New expenditure = \(12 \times (1 + 0.20) = 12 \times 1.2 = 14.4\) parts

**For Daal:**
- Original expenditure = 17 parts
- New expenditure = \(17 \times (1 + 0.30) = 17 \times 1.3 = 22.1\) parts

**For Wheat:**
- Original expenditure = 3 parts
- New expenditure = \(3 \times (1 + 0.50) = 3 \times 1.5 = 4.5\) parts

### Step 5: Calculate the Total New Expenditure
Now, we sum the new expenditures:
\[ \text{Total New Expenditure} = 14.4 + 22.1 + 4.5 = 41 \text{ parts} \]

### Step 6: Calculate the Increase in Expenditure
To find the increase in expenditure, we subtract the total original expenditure from the total new expenditure:
\[ \text{Increase in Expenditure} = \text{Total New Expenditure} - \text{Total Original Expenditure} = 41 - 32 = 9 \text{ parts} \]

### Step 7: Calculate the Percentage Increase in Expenditure
Finally, we calculate the percentage increase in expenditure:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase in Expenditure}}{\text{Total Original Expenditure}}\right) \times 100 = \left(\frac{9}{32}\right) \times 100 \approx 28.125\% \]

### Final Answer
The expenditure of the family will increase by approximately **28.125%**.

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