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 the length of his total journey be x

According to question,

2/5x + 1/3x + 1/4x + 3 = x

59/60x + 3 = x

x / 60 = 3

x = 180km

Therefore, length of total journey be 180km.

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Answer 2

|| SOLUTION ||

Let total distance travelled be x km.

$\\ \\ \bold{Distance \: travelled \: by \: train = \frac{2}{5} \: of \: x \: = \frac{2x}{5} } \\ \\ \bold{Distance \: travelled \: by \: bus = \frac{1}{3} \: of \: x = \frac{x}{3} } \: \: \: \\ \\ \bold{Distance \: travelled \: by \: car = \frac{1}{4} \: of \: x = \frac{x}{4} } \: \: \: \: \\ \\ \bold{ Distance \: travelled \: by \: foot = 3km} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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According to the Question,

$\\ \\ \therefore\bf{ \frac{2x}{5} + \frac{x}{3} + \frac{x}{4} + 3 = x } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \bf{ \frac{(2x \times 12) + (20x) + (15x) + (3 \times 60)}{60} = x } \\ \\ \implies \bf{ \frac{24x + 20 x + 15x + 180}{60} } = x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bf{ \frac{59x + 180}{60} = x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bf{59x + 180 = 60x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bf{180 = 60x - 59x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \bf \: {x = 180} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\boxed{ \pink\therefore\bf \: The \: total \: distance \: of \: the \: journey \: is \: 180 km}$