This question asks us to find the approximate average price per litre of edible oil over four years, given the price per litre for each year and the condition that an equal amount of money was spent each year.

Understanding the Average Price Calculation

When the amount of money spent is the same each time, but the price varies, the average price is not a simple arithmetic mean. Instead, it's calculated based on the total money spent divided by the total quantity purchased. This scenario is related to the concept of the harmonic mean.

Step-by-Step Calculation of Average Oil Price

Let's break down the calculation:

• Identify the prices: The prices per litre in the four consecutive years are:
  • Year 1: \(P_1 = 150\) rupees/litre
  • Year 2: \(P_2 = 200\) rupees/litre
  • Year 3: \(P_3 = 250\) rupees/litre
  • Year 4: \(P_4 = 300\) rupees/litre
• Assume equal expenditure: Let the amount of money spent in each year be \(M\). Since the expenditure is equal, the total money spent over four years is \(4M\).
• Calculate quantity purchased each year: The quantity of oil purchased in each year is the amount spent divided by the price per litre.
  • Quantity in Year 1: \(Q_1 = \frac{M}{P_1} = \frac{M}{150}\) litres
  • Quantity in Year 2: \(Q_2 = \frac{M}{P_2} = \frac{M}{200}\) litres
  • Quantity in Year 3: \(Q_3 = \frac{M}{P_3} = \frac{M}{250}\) litres
  • Quantity in Year 4: \(Q_4 = \frac{M}{P_4} = \frac{M}{300}\) litres
• Calculate total quantity purchased: The total quantity is the sum of quantities from all four years. \(\text{Total Quantity} = Q_1 + Q_2 + Q_3 + Q_4\) \(\text{Total Quantity} = \frac{M}{150} + \frac{M}{200} + \frac{M}{250} + \frac{M}{300}\) \(\text{Total Quantity} = M \left( \frac{1}{150} + \frac{1}{200} + \frac{1}{250} + \frac{1}{300} \right)\)
• Find the sum of fractions: To add the fractions, we find a common denominator. The Least Common Multiple (LCM) of 150, 200, 250, and 300 is 3000. \(\frac{1}{150} = \frac{20}{3000}\) \(\frac{1}{200} = \frac{15}{3000}\) \(\frac{1}{250} = \frac{12}{3000}\) \(\frac{1}{300} = \frac{10}{3000}\) Sum of fractions = \(\frac{20 + 15 + 12 + 10}{3000} = \frac{57}{3000}\) So, \(\text{Total Quantity} = M \left( \frac{57}{3000} \right)\) litres.
• Calculate the average price: The average price is the total money spent divided by the total quantity purchased. \(\text{Average Price} = \frac{\text{Total Money Spent}}{\text{Total Quantity}}\) \(\text{Average Price} = \frac{4M}{M \left( \frac{57}{3000} \right)}\) We can cancel out \( M \): \(\text{Average Price} = \frac{4}{\frac{57}{3000}}\) \(\text{Average Price} = 4 \times \frac{3000}{57}\) \(\text{Average Price} = \frac{12000}{57}\)
• Approximate the result: Now, we calculate the numerical value. \(\frac{12000}{57} \approx 210.526\) rupees/litre.

Conclusion on Average Price

Rounding the result to the nearest whole number, the approximate average price of oil is 210 rupees per litre.