Question

A person invested sum of Rs. 2600 in different parts at $4\%,6\%and8\%$ per annum simple interest. At the end of the year, he got the same interest in all three cases. The money invested at $4\%$ is:

• A. Rs. 2200
• B. Rs. 800
• C. Rs. 1600
• D. Rs. 1200

Answer 1

The correct option is D Rs. 1200

Let x , y and x be his investments at $4\%,6\%and8\%$ respectively
Simple Interest on x at $4\%$ for 1 year
= Simple Interest on y at $6\%$ for 1 year
= Simple Interest on z at $8\%$ for 1 year
$\frac{(x\times 4\times 1)}{100}=\frac{(y\times 6\times 1)}{100}=\frac{z\times 8\times 1}{100}$
$\Rightarrow$ 4x = 6y = 8z
$\Rightarrow$ 2x = 3y = 4z
Hence, we have $y=\frac{2x}{3}andz=\frac{2x}{4}=\frac{x}{2}$
We know that x + y + z = Rs. 2600
$\Rightarrow x+\left(\frac{2x}{3}\right)+\left(\frac{x}{2}\right)=Rs.2600$
$\Rightarrow$ 6x + 4x + 3x = 2600 $\times$ 6
$\Rightarrow$ 13x = 2600 $\times$ 6
$\Rightarrow x=\frac{(2600\times 6)}{13}=200\times 6=Rs.1200$
i.e. Money invested at $4\%$ = Rs. 1200