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?

• A. $180$
• B. $150$
• C. $120$
• D. $140$

Answer 1

The correct option is A ($180$)

Let the length of his total journey be $x$

Journey travelled by train $=\frac{2}{5}x$
Journey travelled by bus$=\frac{1}{3}x$
Journey travelled by car $=\frac{1}{4}x$
remaining travelled by foot$=3km$
So, $\frac{2}{5}x+\frac{1}{3}x+\frac{1}{4}x+3=x$

$x(\frac{2}{5}+\frac{1}{3}+\frac{1}{4})-x=-3$

$x(\frac{2}{5}+\frac{1}{3}+\frac{1}{4}-1)=-3$

$x\left(\frac{(2\times 12)+20+(1\times 15)-60}{60}\right)=-3$

$x\left(\frac{24+20+15-60}{60}\right)=-3$

$x\left(\frac{-1}{60}\right)=-3$

$\frac{x}{60}=3$

$\therefore x=180km$