Question : What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 8 years and 20 years?
Option 1: 5 : 7
Option 2: 2 : 5
Option 3: 3 : 5
Option 4: 4 : 3
Correct Answer: 2 : 5
Solution :
Principal = P for both cases
Rate = R for both cases
Time = 8 years for 1st case, 20 years for 2nd case.
Now,
Simple interest for 1st case : Simple interest for 2nd case
= $\frac{\text{Principal × Rate × Time}}{100}$ : $\frac{\text{Principal × Rate × Time}}{100}$
= $\frac{\text{P × R × 8}}{100}$ : $\frac{\text{P × R × 20}}{100}$
= $8 : 20$
= $2 : 5$
Hence, the correct answer is 2 : 5.
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