Question : A money lender lent INR 30,000 in two parts, one at the rate of 8% and the other at 9%. If the total annual simple interest on the amount is 2650, then what is the amount of money lent at the rate of 8%?
Option 1: INR 6,000
Option 2: INR 5,000
Option 3: INR 4,500
Option 4: INR 5,500
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Correct Answer: INR 5,000
Solution :
Given: Principal = INR 30000
Let the money lent at 8% be Rs. $x$, and the money lent at 9% be $(300000-x)$,
and the time be 1 year.
According to the question,
Simple interest on $x$ at 8% + simple interest on $(30000-x)$ at 9% = 2650
⇒ $\frac{x \times 8 \times 1}{100}+ \frac{(30000-x) \times 9 \times 1}{100}=2650$
⇒ $\frac{8x}{100}+ \frac{270000-9x}{100}=2650$
⇒ $ \frac{8x+270000-9x}{100}=2650$
⇒ $8x+270000-9x=265000$
$\therefore x=5000$
Hence, the correct answer is INR 5,000.
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