Question

A man travelled two-fifth of his journey by train, one-third by bus, one-fourth by car and the remaining $3km$ on foot. What is the length of his total journey?

Answer 1

Let his total journey length be $x$.
Given distance travelled by train = $\frac{2}{5}x$,
distance travelled by bus = $\frac{1}{3}x$
and distance travelled by car=$\frac{1}{4}x$
$\therefore$ Total journey travelled by train, bus and car = $\frac{2}{5}x+\frac{1}{3}x+\frac{1}{4}x$
$=\frac{(12\times 2x)+(20\times x)+(15\times x)}{60}$ [$\because \text{LCM~of~}5,3\text{and}4=60]$
$=\frac{24x+20x+15x}{60}=\frac{59x}{60}$
Therefore, Remaining journey $=\frac{60x}{60}-\frac{59x}{60}=\frac{60x-59x}{60}=\frac{x}{60}$

According to the question, remaining journey is $3km$.
$\therefore \frac{x}{60}=3$
$\Rightarrow x=3\times 60=180km.$
Hence, the length of his total journey is $180km$.