There are 3 types of expenditure in a car. Ist raw material, IInd labour expenditure, IIIrd is extra expenditure. The ratio of these expenditure are 4:3:2. If Ist expenditure is increased by 10%, IInd is increased by 8% and IIIrd is decreased by 5%. Find the percentage change in price of car.

Options

A. `4%`
B. `2%`
C. `5%`
D. `6%`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given ratio of expenditures
The expenditures are given in the ratio of 4:3:2 for raw material, labour, and extra expenditure respectively.

### Step 2: Assign values based on the ratio
Let us assume a common factor \( K \) for the ratio. Therefore:
- Raw Material Expenditure = \( 4K \)
- Labour Expenditure = \( 3K \)
- Extra Expenditure = \( 2K \)

### Step 3: Calculate the total initial expenditure
Now, we can calculate the total initial expenditure (which is also the price of the car):
\[ \text{Total Expenditure} = 4K + 3K + 2K = 9K \]

### Step 4: Calculate the new expenditures after the changes
1. **Raw Material Expenditure**: Increased by 10%
\[ \text{New Raw Material Expenditure} = 4K + 0.10 \times 4K = 4K + 0.4K = 4.4K \]

2. **Labour Expenditure**: Increased by 8%
\[ \text{New Labour Expenditure} = 3K + 0.08 \times 3K = 3K + 0.24K = 3.24K \]

3. **Extra Expenditure**: Decreased by 5%
\[ \text{New Extra Expenditure} = 2K - 0.05 \times 2K = 2K - 0.1K = 1.9K \]

### Step 5: Calculate the total new expenditure
Now, we can calculate the total new expenditure:
\[ \text{New Total Expenditure} = 4.4K + 3.24K + 1.9K = 9.54K \]

### Step 6: Calculate the percentage change in price
To find the percentage change in price, we use the formula:
\[ \text{Percentage Change} = \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \frac{9.54K - 9K}{9K} \times 100 = \frac{0.54K}{9K} \times 100 = \frac{54}{9} = 6\% \]

### Final Answer
The percentage change in the price of the car is **6%**.

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