Shortcut Trick Average cost is the total money spent divided by the total quantity bought. Total amount spent = 3 × 6783 = Rs. 20349 Total quantity = (6783 ÷ 17) + (6783 ÷ 19) + (6783 ÷ 21) = 399 + 357 + 323 = 1079 liters Average cost = 20349 ÷ 1079 ≈ Rs. 18.85 ∴ The correct answer is Rs. 18.85. Alternate Method Given: Amount spent per year = Rs. 6783 Prices per liter for 3 consecutive years = Rs. 17, Rs. 19, and Rs. 21 Formula Used: Average Cost = Total Amount Spent ÷ Total Quantity Year 1 ₹ 6783 @ ₹ 17/L 399 L Year 2 ₹ 6783 @ ₹ 19/L 357 L Year 3 ₹ 6783 @ ₹ 21/L 323 L • Total Spend = ₹ 20349 Total Quantity = 1079 L Calculations: ⇒ Total amount spent in 3 years = 6783 × 3 = Rs. 20349 ⇒ Quantity bought in 1st year = 6783 ÷ 17 = 399 liters ⇒ Quantity bought in 2nd year = 6783 ÷ 19 = 357 liters ⇒ Quantity bought in 3rd year = 6783 ÷ 21 = 323 liters ⇒ Total quantity of gasoline = 399 + 357 + 323 = 1079 liters ⇒ Average cost per liter = 20349 ÷ 1079 ⇒ Average cost per liter = 18.859... ⇒ Average cost per liter ≈ Rs. 18.85 ∴ The correct answer is Rs. 18.85. Related Concepts: Harmonic Mean for Averages When a constant total amount is spent on items with varying prices, the overall average price is derived using the Harmonic Mean of the individual prices: Average = n ÷ (1/a + 1/b + 1/c ...). Average Speed Analogy This concept is strictly identical to calculating average speed when equal distances are covered at different speeds (since Speed = Distance ÷ Time mathematically equals Price = Amount ÷ Quantity). Weighted Average If varying amounts were spent across the different years, the general formula directly applies: Weighted Average = (Amount_(1) + Amount_(2) + ...) ÷ (Quantity_(1) + Quantity_(2) + ...).