Question
A certain sum was invested at simple interest. After 5
years, it became (117/ ninety) times the amount it had reached in 3 years. Find the annual rate of interest.Solution
ATQ,
Let the rate of interest be ‘r%’ p.a.
Let the amount after 3 years = Rs. ‘90x’
So, amount after 5 years = (117/90) × 90x = Rs. ‘117x’
Interest in 2 years = 117x – 90x = Rs. ‘27x’
So, yearly interest = 27x / 2 = Rs. ‘13.5x’
Principal = 90x – 13.5x × 3 = Rs. ‘49.5x’
ATQ,
49.5x × (r / 100) × 1 = 13.5x
r = (13.5x × 100) / 49.5x = 27.27
The rate of interest = r = 27.27%
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