Question

Biju who lives in a town has to travel 3/4 of his journey by train 1/8 by car 1/12 by cart and the remaining 4km by foot to reach his village l. How far is his village from the town

Answer 1

let distance between town and village be x
then,X-(3X/4+X/8+X/12)=4
X-(23X/24)=4
X/24=4
X=96
So, distance is 96

Answer 2

The answer is 96km

GIVEN

Biju who lives in a town has to travel 3/4 of his journey by train 1/8 by car 1/12 by cart and the remaining 4km by foot to reach his village.

TO FIND

Distance of village from the town.

SOLUTION

We can simply solve the above problem as follows;

Let the distance between village and town = x km

Distance travelled by train = 3x/4 km

Distance travelled by car = x/8 km

Distance travelled by cart = x/12 km

Distance travelled on foot = 4 km

Total distance would be equal to the sum of the fractions of distances travelled through various modes.

Therefore,

$\frac{3x}{4} + \frac{x}{8} + \frac{x}{12} + 4 = x$

LCM of 3, 8,12 = 24

$\frac{18x + 3x + 2x + 96}{24} = x$

Adding the like terms and bringing 24 to RHS

23x + 96 = 24x

96 = 24x-23x

x = 96 km

Hence, The answer is 96km

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