Question : A person invested a sum of INR 18,600 at $x$% p.a. and another sum that is twice the former at ($x$ + 2)% p.a., both at simple interest. If the total interest earned on both investments for $3 \frac{1}{2}$ years is INR 23,110.50, then the rate of interest p.a. on the second investment is:
Option 1: 11%
Option 2: 12.5%
Option 3: 10.5%
Option 4: 13%
Correct Answer: 12.5%
Solution :
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
According to the question:
Total Simple interest = 23110.50
$\Rightarrow \frac{18600 \times x \times 7}{100 \times 2} + \frac{2 \times 18600 \times (x + 2) \times 7}{100 \times 2} = 23110.50$
$\Rightarrow 186 \times x \times 7 + 2 \times 186 \times (x + 2) \times 7 =23110.50 \times 2$
$\Rightarrow x= 10.5\%$
Rate of interest on the second investment = $x + 2 = 10.5 + 2 = 12.5\%$
Hence the correct answer is 12.5%.
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