Question : A person invested a total sum of Rs. 15,500 in three schemes of simple interest at the annual rate of 4 percent, 6 percent, and 10 percent. At the end of one year, he got the same interest in all three schemes. What is the sum invested at the rate of 6 percent?
Option 1: Rs. 5400
Option 2: Rs. 5000
Option 3: Rs. 5500
Option 4: Rs. 6500
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Correct Answer: Rs. 5000
Solution : Total investment = Rs. 15,500 The annual rates of simple interest for these schemes are 4%, 6%, and 10%, respectively. Let's denote the sums invested in the schemes with rates of 4%, 6%, and 10% as P 1 , P 2 , and P 3 , respectively. We know that P 1 + P 2 + P 3 = Rs. 15,500 Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ We are also given that the interest earned from these investments after one year is the same. So, $\frac{P_1 \times 4}{100} = \frac{P_2 \times 6}{100} = \frac{P_3 \times 10}{100}$ ⇒ $4P_1=6P_2=10P_3$ So, $P_1:P_2:P_3 = 15:10:6$ ⇒ $P_2 = \frac{10}{31}×15500$ ⇒ $P_2=5000$ Hence, the correct answer is Rs. 5000.
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