CA Foundation · Quantitative Aptitude · Sequence and Series
Mehta Traders buys a machine whose value falls each year. A donation fund pays ₹6,000 in the first year, and each later year's payment is 3/4 of the previous year's payment, continuing forever. What is the present total of all payments ignoring interest, and by how much does the total of the first 2 years fall short of it?
The total of all payments is ₹24,000, from 6,000 divided by 1/4. The first two years give 6,000 + 4,500 = 10,500, so the shortfall is 24,000 - 10,500 = ₹13,500.
- A₹24,000 and ₹16,500 short
- B₹24,000 and ₹10,500 shortCorrect
- C₹18,000 and ₹10,500 short
- D₹24,000 and ₹13,500 short
Explanation
Sum to infinity = 6000/(1 - 3/4) = 24,000. First two payments = 6000 + 4500 = 10,500. Shortfall = 24,000 - 10,500 = 13,500, so the correct option must say 13,500.
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