Question

56 is divided into two parts in such a way that $\frac{6}{5}$ of one part is equal to $\frac{2}{3}$ of the other. What would be the smaller part?

Answer 1

Let one part be $x$.

Then, other part = $56-x$

Given that
$\frac{6}{5}$ of one part = $\frac{2}{3}$ of the other
$\Rightarrow \frac{6}{5}x=\frac{2}{3}(56-x)$
$\Rightarrow 18x=10(56-x)$
$\Rightarrow 18x=560-10x$
$\Rightarrow 28x=560$
$\Rightarrow x=20$

The other part would be 56 - 20 = 36
Hence, the smaller part is 20.