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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?
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Solution
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.
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