Question : In a certain duration of time, a sum becomes 2 times itself at the rate of 5% per annum simple interest. What will be the rate of interest if the same sum becomes 5 times itself in the same duration?
Option 1: 20%
Option 2: 16%
Option 3: 10%
Option 4: 18%
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Correct Answer: 20%
Solution :
Rate, $R$ = 5%
Let $P$ be the principal sum and $n$ be the time.
Amount = $2P$
Simple interest, SI = $2P - P$ = $P$
Now, SI = $\frac{PnR}{100}$
⇒ $P$ = $\frac{P×n×5}{100}$
⇒ $n$ = 20 years
Again, Amount = $5P$
SI = $5P - P$ = $4P$
Now, SI = $\frac{PnR}{100}$
⇒ $4P$ = $\frac{P×20×R}{100}$
⇒ $R$ = 4 × 5 = 20%
Hence, the correct answer is 20%.
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