Question : A certain amount will become six times in 20 years. How long does it take for the same amount to become 5 times?(Assume the same rate of simple interest in each case)
Option 1: 16 years 8 months
Option 2: 15 years 8 months
Option 3: 15 years
Option 4: 16 years
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Correct Answer: 16 years
Solution :
Let $P$ be the principal amount and $R$ be the rate of interest.
Term, $n$ = 20 years
Total amount = $6P$
Simple interest, SI = $6P – P$ = $5P$
SI = $\frac{P×n×R}{100}$
⇒ $5P$ = $\frac{P×20×R}{100}$
⇒ $R$ = 25%
Again, the total amount = $5P$
Simple interest, SI = $5P – P$ = $4P$
SI = $\frac{P×n×R}{100}$
⇒ 4P = $\frac{P×n×25}{100}$
⇒ $n$ = 16 years
Hence, the correct answer is 16 years.
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