Question : A certain amount is lent at $x$% p.a. simple interest for 3 years. Instead, if the amount was lent at $3x$% p.a. simple interest for $y$ more years, the simple interest would have been seven times the earlier interest. What is the value of $y?$
Option 1: 3
Option 2: 4
Option 3: 5
Option 4: 6
Correct Answer: 4
Solution :
Given: A certain amount is lent at $x$% p.a. simple interest for 3 years.
Simple interest $=\frac{\text{Principal × Rate × Time}}{100}$
Simple interest for 3 years $=\frac{100\times x\times 3}{100} = 3x$
Then, simple interest for $y$ more years is given as,
$\frac{100\times3x\times (3+y)}{100} = 7×3x$
⇒ $9x + 3xy = 21x$
⇒ $3xy = 12x$
⇒ $y = 4$
Hence, the correct answer is $4$.
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