Question

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

Answer 1

Let his total journey length be x.

∴ Then, travelled by train = `2/5x`,

 Travelled by bus = `1/3x` and travelled by car = `1/4x`

∴ Total journey travelled by train, bus and car = `2/5x + 1/3x + 1/4x`

= `(12 xx 2x + 20 xx x + 15 xx x)/60` ...[∵ LCM = of 5, 3 and 4 = 60]

= `(24x + 20x + 15x)/60`

= `(59x)/60`

∴ Remaining journey = `x/1 - (59x)/60`

= `(60x - 59x)/60`

= `x/60`

According to the question,

Remaining journey is 3 km.

∴ `x/60 = 3`

⇒ x = 3 × 60 = 180 km  ...[By cross-multiplication]

Hence, the length of his total journey is 180 km.