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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Arithmetic Progression and Geometric Progression

A machine bought by Sharma Industries for Rs 80,000 loses value so that its value at the end of each year is 75% of the value at the start of that year. What is its value at the end of 3 years?

The machine value falls by a constant ratio of 0.75 each year, so it follows a geometric progression. After three years it is 80,000 x 27/64, which equals Rs 33,750. Deducting a fixed 25% of cost yearly would be incorrect.

  1. ARs 33,750Correct
  2. BRs 20,000
  3. CRs 45,000
  4. DRs 60,000

Explanation

The values form a GP with ratio 0.75. After 3 years value = 80,000 x (3/4)^3 = 80,000 x 27/64 = 1,250 x 27 = Rs 33,750. Rs 20,000 would come from straight-line deduction of 25% of the cost each year, which is a wrong method here.

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