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Let's go through the questions one by one based on the provided image:

### (a) Diesel expenditure in 2006
The factory spends RM 9,000 per week on diesel in 2008. The price index for diesel in 2008 is 150, and we are asked to find the equivalent expenditure for diesel in 2006, when the price index was 100 (as price indices are relative to the base year 2006).

Using the formula:
\[
\text{Expenditure in 2006} = \frac{\text{Expenditure in 2008}}{\text{Price Index in 2008}} \times 100
\]
Substitute the values:
\[
\text{Expenditure in 2006} = \frac{9000}{150} \times 100 = 6000 \text{ RM}
\]
So, the expenditure on diesel in 2006 would be RM 6,000.

### (b) Composite Index Calculation (2008 based on 2006)
The composite index for fuel is calculated based on the weighted average of the price indices and the proportions given in the pie chart.

From Diagram 13:
- Diesel: 180° (i.e., 50% of fuel usage)
- Petrol: 108° (i.e., 30% of fuel usage)
- Gas: 72° (i.e., 20% of fuel usage)

Given price indices:
- Diesel = 150
- Petrol = 120
- Gas = 110

We calculate the composite index using the formula:
\[
\text{Composite Index} = \left( \frac{\text{Weight of Diesel}}{360} \times \text{Diesel Index} \right) + \left( \frac{\text{Weight of Petrol}}{360} \times \text{Petrol Index} \right) + \left( \frac{\text{Weight of Gas}}{360} \times \text{Gas Index} \right)
\]
Substitute values:
\[
\text{Composite Index} = \left( \frac{180}{360} \times 150 \right) + \left( \frac{108}{360} \times 120 \right) + \left( \frac{72}{360} \times 110 \right)
\]
\[
= 75 + 36 + 22 = 133
\]
The composite index is 133.

### (c) Fuel Expenditure in 2008
The factory's fuel expenditure in 2006 is RM 30,000 per week. We need to calculate the equivalent fuel expenditure in 2008 using the composite index calculated in part (b), which is 133.

Using the formula:
\[
\text{Expenditure in 2008} = \frac{\text{Expenditure in 2006} \times \text{Composite Index}}{100}
\]
Substitute values:
\[
\text{Expenditure in 2008} = \frac{30,000 \times 133}{100} = 39,900 \text{ RM}
\]
So, the expenditure in 2008 would be RM 39,900 per week.

### (d) Composite Index (2008 to 2010)
In this part, the price changes from 2008 to 2010 are given:
- Diesel increases by 30%
- Petrol increases by 20%
- Gas price remains unchanged

We need to calculate the new composite index for 2010 using these new prices.

For diesel, petrol, and gas:
\[
\text{Diesel (2010)} = 150 \times 1.30 = 195
\]
\[
\text{Petrol (2010)} = 120 \times 1.20 = 144
\]
\[
\text{Gas (2010)} = 110 \times 1.00 = 110
\]

Using the same weights as in part (b), the new composite index for 2010 is:
\[
\text{Composite Index (2010)} = \left( \frac{180}{360} \times 195 \right) + \left( \frac{108}{360} \times 144 \right) + \left( \frac{72}{360} \times 110 \right)
\]
\[
= 97.5 + 43.2 + 22 = 162.7
\]
The new composite index in 2010 is approximately 162.7.

---

Let me know if you'd like further details, and here are some follow-up questions to expand on this:

1. How do you calculate the price index when given different base years?
2. What other methods can be used to determine inflation effects on expenditure?
3. How do price indices relate to real and nominal prices in economics?
4. What assumptions do we make when calculating composite indices?
5. How would changes in fuel proportions affect the composite index?

**Tip:** When calculating weighted averages, ensure that the weights (like proportions) always sum up to 1 or 100%.

SPM 2011 Question 13: If the factory spends RM9,000 per week for diesel in the year 2008, find the corresponding expenditure for diesel in the year 2006. Calculate the composite index for the fuel expenditure of the factory in the year 2008 based on the year 2006. The fuel expenditure used by the factory is RM30,000 per week in the year 2006. Calculate its corresponding fuel expenditure in the year 2008. The price of diesel increases by 30%, the price of petrol increases by 20% while the price of gas remains unchanged from the year 2008 to the year 2010. Calculate the composite index for the fuel price expenditure of the factory in the year 2010 based on the year 2006.

Learn to solve a composite index and expenditure calculation problem based on SPM 2011. This problem involves price indices, weighted averages, and calculating percentage increases in a factory's fuel costs from 2006 to 2010. Suitable for Grade 11-12 students.

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