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%

Question

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%

Team Careers360 · Accepted Answer

Correct Answer: 12.5%

Solution : Simple interest = $\frac{ ext{Principal × Rate × Time}}{100}$
According to the question:
Total Simple interest = 23110.50
$\Rightarrow \frac{18600 imes x imes 7}{100 imes 2} + \frac{2 imes 18600 imes (x + 2) imes 7}{100 imes 2} = 23110.50$
$\Rightarrow 186 imes x imes 7 + 2 imes 186 imes (x + 2) imes 7 =23110.50 imes 2$
$\Rightarrow x= 10.5\%$
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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