Question : A man travels $\frac{3}{4}$th of the distance of his journey by bus, $\frac{1}{6}$th by rickshaw and the remaining 2 km on foot. The total distance travelled by the man is:
Option 1: 12 km
Option 2: 18 km
Option 3: 20 km
Option 4: 24 km
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Correct Answer: 24 km
Solution :
Given: A man travelled by bus $\frac{3}{4}$th of the total distance.
The man travelled by rickshaw $\frac{1}{6}$th of the total distance.
The man travelled on foot = 2 km
Let the total distance to be $x$ km.
So, the remaining distance $=x-\frac{3x}{4}-\frac{x}{6}$
According to the question,
$x-\frac{3x}{4}-\frac{x}{6} = 2$
$⇒\frac{12x-9x-2x}{12}=2$
$⇒\frac{x}{12}=2$
$\therefore x=24$
Hence, the correct answer is 24 km.
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