Question

A person invested sum of ₹ 2600 in different parts at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all three cases. Then the money invested at 4% is ₹ 1200.

• A. Rs. 2200
• B. Rs. 800

Answer 1

The correct option is A Rs. 2200

Let $x,y$ and $z$ be his investments at 4%, 6% and 8% respectively.
Given, 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

We know that S.I. = $\frac{PRT}{100}$

where, S.I. is the simple interest, P is the principal, R is the rate of interest per annum and T is the time(number of years).

So, $\frac{x\times 4\times 1}{100}=\frac{y\times 6\times 1}{100}=\frac{z\times 8\times 1}{100}$
$\Rightarrow 4x=6y=8z$
$\Rightarrow 2x=3y=4z$
Hence, we have $y=\frac{2x}{3}andz=\frac{2x}{4}=\frac{x}{2}$
Given $x+y+z=2600$
$\Rightarrow x+\left(\frac{2x}{3}\right)+\left(\frac{x}{2}\right)=₹2600$
$\Rightarrow 6x+4x+3x=2600\times 6$
$\Rightarrow 13x=2600\times 6$
$\Rightarrow x=\frac{(2600\times 6)}{13}=200\times 6=₹1200$
i.e. Money invested at 4% = ₹ 1200