At a certain rate of simple interest, the ratio of the sum and the amount for a certain period of time is 4 : 5. After 3 more years, the ratio becomes 5 : 7. The rate of interest is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5%
The sum (principal) is the same in both ratios, so the two ratios are first written with the same principal. Then the extra interest earned in the 3 more years can be read off, and simple interest is the same every year.
Making the principal equal (LCM of 4 and 5 is 20):
Sum : Amount \(=4:5=20:25\), so the interest for the first period is \(25-20=5\) parts
Sum : Amount \(=5:7=20:28\), so the interest after 3 more years is \(28-20=8\) parts
Rate of interest (principal 20 parts):
Interest for the 3 more years \(=8-5=3\) parts, that is, 1 part a year
Rate \(\displaystyle =\frac{1}{20}\times100=5\%\) a year