Question : At a certain annual rate (rounded off to the nearest integer) of simple interest, a sum of money becomes nine times its original value in 21 years. By how much does the rate of interest change if the same sum of money has to become 12 times its original value in 25 years?
Option 1: Decreases by 6%
Option 2: Increases by 6%
Option 3: Increases by 8%
Option 4: Decreases by 8%
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Correct Answer: Increases by 6%
Solution :
Let the principal be $x$.
In 21 years the simple interest is $9x-x=8x$
In 25 years the simple interest is $12x-x=11x$
Case I: Time = 21 years
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ Rate = $\frac{8x×100}{21x}$
⇒ Rate = $\frac{800}{21}\approx$ 38%
Case Il: Time = 25 years
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ Rate = $\frac{11x×100}{25x}$
⇒ Rate = $\frac{1100}{25}$= 44%
⇒ Increase = (44 – 38)% = 6%
Hence, the correct answer is increases by 6%.
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