Question

A man traveled ${\frac{2}{5}}^{\text{th}}$ of his journey by train, ${\frac{1}{3}}^{\text{rd}}$ by taxi, ${\frac{1}{6}}^{\text{th}}$ by bus and remaining $10km$ on foot. Find the length (in $km$) of his total journey.

Answer 1

Let the total length covered of his journey be $x$

$\Rightarrow$ length covered by train $=\frac{2x}{5}$

length covered by taxi $=\frac{x}{3}$

length covered by bus $=\frac{x}{6}$

length covered by foot $=10km$

According to question,
$\Rightarrow \frac{2x}{5}+\frac{x}{3}+\frac{x}{6}+10=x$

LCM of $5,3,6$ is $30$

$\Rightarrow \frac{12x+10x+5x+300}{30}=x$

$\Rightarrow \frac{27x+300}{30}=x$

$\Rightarrow 27x+300=30x$

$\Rightarrow 300=30x-27x$

$\Rightarrow 300=3x$

$\Rightarrow \frac{300}{3}=x$

$\Rightarrow 100=x$

$\Rightarrow x=100$

Therefore, the total length covered in his journey is $100km$.