Calculating the Average Cost Per Litre of Petrol Over Three Years

Suppose a car owner purchases petrol at varying prices per litre over a period of three successive years. Specifically, the owner spends 4000 Euros each year, with the cost per litre being Euro 7.50, Euro 8.00, and Euro 8.50 in the respective years. This calculation focuses on determining the average cost per litre of petrol over the three-year period.

Step-by-Step Calculation

The first step involves calculating the quantity of petrol purchased each year. Using the given information, we follow this process:

For Year 1: The cost per litre is Euro 7.50. Therefore, the quantity of petrol bought is 4000 / 7.50 ≈ 533.33 litres. For Year 2: The cost per litre is Euro 8.00. Thus, the quantity of petrol bought is 4000 / 8.00 500 litres. For Year 3: The cost per litre is Euro 8.50. Consequently, the quantity of petrol bought is 4000 / 8.50 ≈ 470.59 litres.

The total number of litres of petrol bought over the three years is calculated by summing these quantities:

Total Litres 533.33 500 470.59 1503.92 litres

The total amount spent over the three years is:

Total Cost 4000 × 3 12000 Euros

To determine the average cost per litre, we use the formula:

Average Cost Total Cost / Total Litres 12000 / 1503.92 ≈ 7.98 Euros per litre

Thus, the average cost per litre of petrol over the three years is approximately 7.98 Euros.

Alternative Methods

Alternatively, consider the following method to calculate the total quantity of petrol consumed over the three years. The calculations are as follows:

Total Quantity of Petrol 4000/7.5 4000/8 4000/8.5 533.33 500 470.588 1503.918 litres Total Expenditure on Petrol for Three Years 4000 × 3 12000 Euros Average Cost of Petrol 12000 / 1503.918 7.98 Euros per litre

General Formula

For a more generalized approach, let x be the yearly spending and a, b, and c be the respective costs per litre in each of the three years. The quantities of petrol purchased over the years would be:

Year 1: x/a Year 2: x/b Year 3: x/c

The total quantity of petrol consumed in three years is:

Total Quantity x/a x/b x/c

The total amount spent over the three years is:

Total Cost 3x

The overall average cost can be found using the formula:

Average Cost Total Cost / Total Quantity 3x / (x/a x/b x/c) 3 / (1/a 1/b 1/c)

Interestingly, the overall average cost is the reciprocal of the average of the reciprocals of the individual costs. This approach provides a theoretical insight into the relationship between individual and average costs.

Conclusion

The average cost per litre of petrol over the period of three years, when purchasing at 7.50 Euros, 8.00 Euros, and 8.50 Euros per litre, is approximately 7.98 Euros per litre. This calculation is useful in understanding the economic impact of fluctuating fuel prices, which can help car owners budget accordingly.