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
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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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