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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