Question : A person lends a certain sum of money at the annual rate of 8% on simple interest and the interest received in 9 years is INR 560 less than the sum lent. What is the sum lent?
Option 1: INR 560
Option 2: INR 1,000
Option 3: INR 2,000
Option 4: INR 1,120
Correct Answer: INR 2,000
Solution :
Given: A person lends a certain sum of money at the annual rate of 8% on simple interest and the interest received in 9 years is INR 560 less than the sum lent.
Use the formula, $SI=\frac{P\times R\times T}{100}$ where $SI$, $P$, $R$, and $T$ are the simple interest, principal, rate, and time.
Let the sum lent be INR $x$.
According to the question,
$x-560=\frac{x\times 8\times 9}{100}$
⇒ $x–560=\frac{18x}{25}$
⇒ $25x-560\times 25=18x$
⇒ $25x-14000=18x$
⇒ $25x-18x=14000$
⇒ $7x=14000$
⇒ $x=$ INR 2,000
Hence, the correct answer is INR 2,000.
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