A car owner buys petrol at Rs. 4, Rs. 5 and Rs. 8 per litre for 3 consecutive years. What is the average cost per litre of petrol if he spends Rs. 40,000 each year?

1. A

   Rs. 4.92

2. B

   Rs. 4.82

3. C

   Rs. 5.22

4. D

   Rs. 5.17

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

• The average cost per unit is calculated by dividing the total expenditure by the total quantity purchased.
• The total expenditure over three years is 3 × Rs. 40,000 = Rs. 1,20,000.
• The total quantity of petrol purchased is the sum of quantities from each year: (40000/4) + (40000/5) + (40000/8) = 10,000 + 8,000 + 5,000 = 23,000 litres.
• Dividing the total expenditure by the total quantity gives the average cost: Rs. 1,20,000 / 23,000 litres = Rs. 5.217, which rounds to Rs. 5.22 per litre.
• This problem is a classic example where the Harmonic Mean gives the correct average price because the amount of money spent is constant.

Why Other Options Were Wrong

• Option A: This value is incorrect. It may result from a calculation error during the division of total cost by total quantity.
• Option B: This is an incorrect calculation. A common mistake is to misuse the prices in the averaging formula.
• Option D: This value is very close to the correct answer but is incorrect. It likely stems from a rounding error or a slight miscalculation during the final division (120,000 / 23,000).

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Average Cost and Harmonic Mean as background academic context rather than a clinical decision trigger.
• Proficiency in mathematical calculations is a fundamental skill for nurses, essential for accurate medication dosage calculations, IV drip rate adjustments, and interpreting patient data charts.
• Understanding different types of averages (e.g., arithmetic mean, harmonic mean) is crucial for correctly interpreting clinical data and research findings.
• What if? If the car owner had purchased an equal quantity of petrol (e.g., 1000 litres) each year, the average cost would be the simple arithmetic mean of the prices: (Rs. 4 + Rs. 5 + Rs. 8) / 3 = Rs. 5.67 per litre. This highlights the importance of identifying whether the quantity or the expenditure is the constant factor.

How to Approach the Question

• First, identify the key information: prices per litre for 3 years (Rs. 4, Rs. 5, Rs. 8) and the constant amount spent each year (Rs. 40,000).
• Recognize that the goal is to find the overall average cost per litre.
• Recall the fundamental formula for average cost: Average Cost = Total Expenditure / Total Quantity.
• Calculate the total expenditure by multiplying the annual spending by the number of years (3 × 40,000).
• For each year, calculate the quantity of petrol purchased by dividing the annual spending by the price for that year.
• Sum the quantities from all three years to find the total quantity purchased.

Concept Tested & Keywords

• Concept Tested: Calculation of Average Cost and Harmonic Mean
• Stem keywords: average cost, petrol, consecutive years, spends Rs. 40,000 each year
• Lead-in keywords: What is the average cost

Question ID

QKgo-6ggcbkUuwm_Df7E8l

Copy ID

Reference Book

E6 NursingResearch Sukhpal Kaur p. 443-445