Problem Analysis

The question provides the cost per litre of a product for three consecutive years and the average amount a person spends annually on this product. The goal is to find the average cost per litre over these three years.

• Year 1 Cost per Litre: Rs. 134
• Year 2 Cost per Litre: Rs. 268
• Year 3 Cost per Litre: Rs. 335
• Average Annual Spending: Rs. 14740

Calculation Strategy

To find the average cost per litre, we need the total amount spent and the total quantity (in litres) purchased over the three years. Since the amount spent per year is constant (Rs. 14740), we can calculate the litres purchased each year and sum them up.

The formula for average cost per litre is:

Step-by-Step Solution

1. Calculate the quantity of the product purchased each year:

   • Year 1 Litres ($L_1$) = $\frac{\text{Annual Spending}}{\text{Cost per Litre (Year 1)}} = \frac{14740}{134} = 110$ litres.
   • Year 2 Litres ($L_2$) = $\frac{\text{Annual Spending}}{\text{Cost per Litre (Year 2)}} = \frac{14740}{268} = 55$ litres.
   • Year 3 Litres ($L_3$) = $\frac{\text{Annual Spending}}{\text{Cost per Litre (Year 3)}} = \frac{14740}{335} = 44$ litres.

2. Calculate the total quantity of the product purchased over three years:

   $ L_{\text{total}} = L_1 + L_2 + L_3 = 110 + 55 + 44 = 209 \text{ litres} $

3. Calculate the total amount spent over three years:

   $ \text{Total Spending} = \text{Average Annual Spending} \times 3 = 14740 \times 3 = 44220 \text{ Rs.} $

4. Calculate the average cost per litre:

   $ \text{Average Cost per Litre} = \frac{\text{Total Spending}}{L_{\text{total}}} = \frac{44220}{209} $ $ \frac{44220}{209} \approx 211.5789... $

5. Final Result:

   The calculated average cost is approximately Rs. 211.5789. Rounding this value to two decimal places results in Rs. 211.58. However, considering the provided options, the value 211.57 is the closest match. The calculation indicates a value very near to this.

   Result ≈ Rs. 211.57