Question

A man travelled two fifths of his journey by train ,one third by bus, one fourth by car and remaining 3 km on foot . what is the length of his total journey

Answer 1

Let the length of the total journey be x km

So, according to the question.

2/5th part is travelled by train = 2x/5 km

1/3rd part is travelled by bus = x/3 km

1/4th part is travelled by the car = x/4 km

Remaining 3 km is travelled by foot = 3 km

⇒ 2x/5 + x/3 + x/4 + 3 = x

Taking L.C.M. of the denominators and then solving it (L.C.M. is 60).

⇒ (24x + 20x + 15x + 180)/60 = x

⇒ (59x + 180)/60 = x

⇒ 59x + 180 = 60x

59x - 60x = - 180

⇒ - x = - 180

⇒ x = 180

Hence, length of the total journey is 180 km

Answer.

Answer 2

Let the Total Distance traveled by the Man during his Journey be : D

Given : The Man traveled two fifths of his journey by Train

$\mathsf{\implies Distance\;traveled\;by\;the\;Man\;by\;Train = (\frac{2}{5} \times D)}$

Given : The Man traveled one third of his Distance by Bus

$\mathsf{\implies Distance\;traveled\;by\;the\;Man\;by\;Bus = (\frac{1}{3} \times D)}$

Given : The Man traveled one fourth of his Distance by Car

$\mathsf{\implies Distance\;traveled\;by\;the\;Man\;by\;Car = (\frac{1}{4} \times D)}$

Given : Remaining Distance traveled by the Man on Foot = 3 km

In order to Solve this Problem, We need to Realize that : The Sum of Distance traveled by the Man using Train - Bus - Car - Foot should be Equal to the Total Distance (D)

$\mathsf{\implies (\frac{2D}{5} + \frac{D}{3} + \frac{D}{4} + 3) = D}$

$\mathsf{\implies (\frac{12(2D) + 20(D) + 15(D) + 180}{60}) = D}$

$\mathsf{\implies {24D + 20D + 15D + 180} = 60D}$

$\mathsf{\implies 60D - 59D = 180}$

$\mathsf{\implies D = 180}$

The Length of his Total Journey is 180 km