What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 12 years?
3:4
To solve this problem, let's analyze the relationship between the simple interest earned over different time periods, keeping the principal amount and the rate of interest constant.
According to the formula for simple interest:
\(SI = \frac{{P \cdot R \cdot T}}{100}\)
where \(SI\) is the Simple Interest, \(P\) is the Principal amount, \(R\) is the Rate of interest per annum, and \(T\) is the Time in years.
Given that the principal amount \(P\) and rate of interest \(R\) are the same for both cases, the simple interest is directly proportional to time \(T\).
Consider:
- Simple Interest for 9 years: \(SI_1 = \frac{{P \cdot R \cdot 9}}{100}\)
- Simple Interest for 12 years: \(SI_2 = \frac{{P \cdot R \cdot 12}}{100}\)
To find the ratio of these interests:
\(Ratio = \frac{SI_1}{SI_2} = \frac{\frac{{P \cdot R \cdot 9}}{100}}{\frac{{P \cdot R \cdot 12}}{100}}\)
Upon simplifying:
\(Ratio = \frac{9}{12} = \frac{3}{4}\)
Thus, the ratio of the simple interest earned for 9 years to that for 12 years is 3:4.
The correct option is therefore 3:4.
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