How to distribute 1000 in two parts such that one part is $\frac{12}{13}$th of the other?

Given:

1000 is distributed in two parts such that one part is $\frac{12}{13}$th of the other. 

To do:

We have to find two parts.

Solution:

Let one of the parts be $x$.

This implies,

The other part$=\frac{12}{13}\times x=\frac{12x}{13}$

According to the question,

$x+\frac{12x}{13}=1000$

$\frac{13x+12x}{13}=1000$

$25x=13\times1000$

$x=\frac{13\times1000}{25}$

$x=13\times40$

$x=520$

$\Rightarrow \frac{12x}{13}=\frac{12\times520}{13}=12\times40=480$

Therefore, the two parts are 520 and 480.