A car owner buys petrol at ₹ 17, ₹ 19 and ₹ 20 per litre for three consecutive years. Compute the average cost per litre, if he spends ₹ 6460 per year.

Concept & Formula When equal amounts of money are spent at different rates, the average rate is given by the Harmonic Mean of the individual rates. Alternatively, it can be calculated as the total money spent divided by the total quantity purchased. $$\text{Average Cost per Litre} = \frac{\text{Total Money Spent}}{\text{Total Quantity Purchased}}$$ Step-by-Step Solution * Given: Expenditure per year = ₹ 6460. * Total money spent over 3 years = $3 \times 6460 = \text{₹ } 19380$. * Quantity purchased in Year 1 = $\frac{6460}{17} = 380$ litres. * Quantity purchased in Year 2 = $\frac{6460}{19} = 340$ litres. * Quantity purchased in Year 3 = $\frac{6460}{20} = 323$ litres. * Total quantity purchased = $380 + 340 + 323 = 1043$ litres. * Average cost per litre = $\frac{19380}{1043} \approx \text{₹ } 18.485$ or ₹ 18.49. Exam Strategy & Shortcut Since the annual expense is fixed at ₹ 6460, the average cost depends purely on the rates themselves and equals their Harmonic Mean: $$\text{Average Rate} = \frac{3}{\frac{1}{17} + \frac{1}{19} + \frac{1}{20}}$$ Approximation tip: The standard arithmetic mean is $(17 + 19 + 20)/3 = 18.67$. The Harmonic Mean is always slightly less than the Arithmetic Mean when numbers vary. Therefore, the answer must be just under 18.67. Option (a) 18.49 fits perfectly without doing full long division. Common Pitfall A frequent trap is calculating the simple arithmetic average of the prices: $(17 + 19 + 20) / 3 = 18.67$. This is mathematically wrong because more litres are bought in the years when petrol is cheaper. Final Answer Therefore, the correct answer is ₹ 18.49.