Question : Rajesh invested INR 10,000 by dividing it into two different investment schemes, A and B, at simple interest rates of 8% and 10%, respectively. If the total interest earned in 2 years is INR 1,680, the amount invested in scheme A is:
Option 1: INR 8,000
Option 2: INR 2,000
Option 3: INR 6,000
Option 4: INR 4,000
Correct Answer: INR 8,000
Solution :
Let the amount invested in scheme A be $x$ and in scheme B be $y$
Rate of A scheme = $\frac{8}{100}$ = 0.08
Rate of B scheme = $\frac{10}{100}$ = 0.10
Total invested amount INR 10,000
⇒ $x + y$ = 10,000
Total interest = ($x$ × 0.08 × 2) + ($y$ × 0.10 × 2) = 1680
⇒ 0.16$x$ + 0.20 $y$ = 1680
⇒ 0.16 $x$ + 0.20(10,000 – $x$) = 1680
⇒ 0.16 $x$ + 2000 − 0.20 $x$ = 1680
⇒ – 0.04 $x$ = 1680 – 2000 = – 320
⇒ $x$ = $\frac{– 320}{ – 0.04}$ = 8000
Hence, the correct answer is INR 8,000.
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