Question : In what least number of complete years does a sum of money become more than four times itself at the rate of 50% per annum on simple interest?
Option 1: 9 years
Option 2: 7 years
Option 3: 6 years
Option 4: 5 years
Correct Answer: 7 years
Solution :
Let's suppose, in $Q$ years a sum of money, say $P$ becomes four times itself at the rate of 50% per annum on simple interest.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
According to the question,
$P+\frac{P(50)(Q)}{100}=4P$
⇒ $\frac{PQ}{2}=4P - P$
⇒ $\frac{Q}{2}=3$
$\therefore Q=6$
So, to become more than four times itself, the principal must take at least 6 + 1 = 7 years
Hence, the correct answer is 7 years.
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