Question

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

Answer 1

let total journey be $xkm$

the journey travelled by train $=\frac{2}{5}x$

the journey travelled by taxi $=\frac{1}{3}x$

the journey travelled by bus$=\frac{1}{6}x$

the journey travelled by foot $=10km$

According to the question, we have

$x-(\frac{2}{5}x+\frac{1}{3}x+\frac{1}{6}x)=10km$

$x-[\frac{2\times 6}{5\times 6}+\frac{1\times 10}{3\times 10}+\frac{1\times 5}{6\times 5}]x=10$ [lcm of denominators $=30$]

$x-[\frac{12}{30}+\frac{10}{30}+\frac{5}{30}]x=10$

$\Rightarrow x-\frac{27x}{30}=10$

$\Rightarrow \frac{3x}{30}=10$

$\therefore x=100$

Hence, the total length of the journey is $100km.$