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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion

A purchase manager in Kolkata spends the same amount of ₹600 on a raw material in each of three months, when the prices are ₹20, ₹30 and ₹60 per kg respectively. What is the average price paid per kg over the three months?

The average price is ₹30 per kg. Equal money is spent each month, so the harmonic mean of the prices applies. Total spend of ₹1,800 buys 30 + 20 + 10 = 60 kg, giving ₹30. The arithmetic mean of ₹36.67 is wrong because it ignores the quantities bought.

  1. A₹30Correct
  2. B₹36.67
  3. C₹32
  4. D₹40

Explanation

Quantities bought are 600/20 = 30 kg, 600/30 = 20 kg and 600/60 = 10 kg, a total of 60 kg. Total spend is ₹1,800, so the average price is 1800/60 = ₹30. This equals the harmonic mean 3/(1/20 + 1/30 + 1/60) = 3/(6/60) = 30. The ₹36.67 option is the simple arithmetic mean of the prices, which is wrong because more kg are bought at the lower prices.

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