Question

Divide $105$ into two parts such that $\frac{1}{3}$ of one part is equal to $\frac{1}{4}$ of another part.

Answer 1

Let one part be $x$ and other part be $y$.

According to question,
$\frac{1}{3}\times x=\frac{1}{4}\times y\Rightarrow x=\frac{3}{4}\times y$
Also, it is given that,
$x+y=105\Rightarrow (\frac{3}{4}+1)y=105\Rightarrow y\times \frac{7}{4}=105\Rightarrow y=\frac{4\times 105}{7}\Rightarrow y=60$
Lets evaluate $x$ by substituting $y=60$ in $x+y=105$,
$x+y=105$
$\Rightarrow x+60=105$
$\Rightarrow x=105-60$
$\Rightarrow x=45$

Therefore, $105$ is divided into two parts as $60$ and $45$ .