Question : A sum of money doubles itself in 7 years at simple interest. In how much time will it become 5 times itself?
Option 1: 25 years
Option 2: 28 years
Option 3: 23 years
Option 4: 21 years
Correct Answer: 28 years
Solution :
Given: Time($T{_1}$) = 7 years
Let, Time($T{_2}$) = $t$ years
Case I
Let the principal be $x$
So, Amount after 7 years = $2x$
Simple interest = Amount – Principal = $2x - x$ = $x$
Interest = Principal
So, $x = \frac{x \times R \times 7}{100}$
⇒ R = $\frac{100}{7}$%
Case II
Amount = $5x$
Interest = $5x - x$ = $4x$
Now, Interest = 4 $\times$ Principal
So, $4x = \frac{x\times\frac{100}{7}\times t}{100}$
⇒ t = $4\times 7 = 28$ years
Hence, the correct answer is 28 years.
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