Question

Divide $34$ into two parts in such a way that ${\left(\frac{4}{7}\right)}^{th}$ of one part is equal to ${\left(\frac{2}{5}\right)}^{th}$ of the other.

Answer 1

Let First part$=x$

then second part$=34-x$

According to the problem,${\left(\frac{4}{7}\right)}^{th}$ of First part$={\left(\frac{2}{5}\right)}^{th}$ of the second part.

$\Rightarrow \frac{4}{7}x=\frac{2}{5}(34-x)$

$\Rightarrow \frac{4x}{7}=\frac{68}{5}-\frac{2x}{5}$

$\Rightarrow \frac{4x}{7}+\frac{2x}{5}=\frac{68}{5}$

$\Rightarrow \frac{4x\times 5}{7\times 5}+\frac{2x\times 7}{5\times 7}=\frac{68}{5}$

$\Rightarrow \frac{20x}{35}+\frac{14x}{35}=\frac{68}{5}$

$\Rightarrow \frac{20x+14x}{35}=\frac{68}{5}$

$\Rightarrow x=14$

Hence two parts are $14$ and $34-14=20$

$\therefore$ the first part is $14$ and second part is $20$