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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