Question : A person invested a total of Rs. 7,900 in three different schemes of simple interest at 3%, 5%, and 8% per annum. At the end of one year, he had the same interest in all three schemes. What is the money (in rupees) invested at 3%?
Option 1: 2900
Option 2: 3500
Option 3: 4000
Option 4: 5600
Correct Answer: 4000
Solution :
Sum = Rs. 7,900
Term, n = 1 year
Let $x$ be the amount invested at 3%, $y$ be the amount invested at 5%, and $z$ be the amount invested at 8%.
$\frac{x×1×3}{100}$ = $\frac{y×1×5}{100}$ = $\frac{z×1×8}{100}$
$⇒3x$ = $5y$ = $8z$
So, $x:y:z=40:24:15$
Divide Rs. 7900 in this ratio. therefore, we get,
$x=\frac{7900}{79}×40$
$\therefore x=4000$
Hence, the correct answer is 4000.
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