A car owner buys petrol at Rs 7.50, Rs 8.00 and Rs 8.50 per litre for three successive years. If he spends Rs 4000 each year on petrol, what is the approximate average cost per litre of petrol over the three years?

Introduction:
This question checks your understanding of weighted average price when the same amount of money is spent at different rates over several periods. It is a very common quantitative aptitude idea used in profit and loss and data interpretation questions.

Given Data / Assumptions:
Petrol price in year 1 = Rs 7.50 per litre. Petrol price in year 2 = Rs 8.00 per litre. Petrol price in year 3 = Rs 8.50 per litre. Amount spent each year = Rs 4000. We need the overall average cost per litre over all three years.

Concept / Approach:
When the money spent is the same, but the price per litre is different, the quantity of petrol purchased each year is different. The correct method is: 1. Compute litres purchased each year. 2. Add all litres to get the total quantity. 3. Divide the total money spent over three years by the total quantity to get the weighted average price.

Step-by-Step Solution:
Step 1: Find litres bought in each year. Year 1: Litres = 4000 / 7.5 ≈ 533.33 litres. Year 2: Litres = 4000 / 8 = 500 litres. Year 3: Litres = 4000 / 8.5 ≈ 470.59 litres. Step 2: Find total litres of petrol. Total litres ≈ 533.33 + 500 + 470.59 ≈ 1503.92 litres. Step 3: Find total money spent. Total money spent in three years = 3 * 4000 = Rs 12000. Step 4: Compute average cost per litre. Average cost per litre ≈ 12000 / 1503.92 ≈ Rs 7.98 per litre.

Verification / Alternative Check:
Notice that all prices are between Rs 7.50 and Rs 8.50, and more litres are bought when petrol is cheaper (Rs 7.50). Therefore, the overall average must be slightly less than the simple average of the three prices. Simple average = (7.5 + 8 + 8.5) / 3 = 8.00. Since more quantity is purchased in the cheapest year, the weighted average should be slightly below 8, which matches Rs 7.98.

Why Other Options Are Wrong:
Rs 6.23 per litre: Far below all three given prices; impossible as an average of higher values. Rs 8.97 per litre: Higher than even the maximum price of Rs 8.50, so it cannot be an overall average. Rs 9.89 per litre: Also greater than all the individual prices, so it is clearly invalid. Rs 7.45 per litre: Below the minimum price of Rs 7.50 and inconsistent with the calculations.

Common Pitfalls:
A common mistake is to simply average the three rates (7.5, 8, 8.5) without considering that the number of litres bought each year is different. Another mistake is to average the three quantities of petrol instead of using the ratio of total money to total quantity. Always use total cost divided by total quantity for such questions.

Final Answer:
The approximate average cost per litre of petrol over the three years is Rs 7.98 per litre.