Question

Mohit travelled $\dfrac{2}{3}$ of his journey by train, $\dfrac{1}{4}$ of his journey by bus and the remaining journey by car. If the distance he travelled by train is $60\text{ km}$ more than the distance he travelled by bus, what was the total distance he had travelled?
(a) $70\text{ km}$
(b) $250\text{ km}$
(c) $144\text{ km}$
(d) $153\text{ km}$

Answer 1

Hint:For solving this question we will first assume the total distance in terms of one variable and then we will frame the equation as per the given data. Then we will solve for that variable and get the correct answer.

Complete step by step answer:
Given:
Mohit travelled $\dfrac{2}{3}$ of his journey by train and $\dfrac{1}{4}$ of his journey by bus and rest by his car. It is given that he travelled 60 km more by train than he travelled by bus.
Now, let the total distance he travelled is $x$ km. Then,
Distance travelled by train = $\dfrac{2}{3}$ (total distance he travelled) $=\dfrac{2x}{3}$ km.
Distance travelled by bus = $\dfrac{1}{4}$ (total distance he travelled) $=\dfrac{x}{4}$ km.
Distance travelled by his car = $x-\dfrac{2x}{3}-\dfrac{x}{4}=\dfrac{x}{12}$ km.
Now, as per the given data, he travelled 60 km more distance by train than the distance he travelled by bus. Then,
Distance travelled by train = Distance travelled by bus + 60 km.
$\dfrac{2x}{3}=\dfrac{x}{4}+60$

$\begin{align}
  & \Rightarrow \dfrac{2x}{3}-\dfrac{x}{4}=60 \\
 & \Rightarrow \dfrac{5x}{12}=60 \\
 & \Rightarrow x=144 \\
\end{align}$
Now, from the above calculations, we can say that he had travelled a total distance of 144 km.
Hence, (c) is the correct option.

Note: Although the question is very easy to solve but the student should frame equations correctly and accordingly as per the given data and avoid doing calculation error while solving for the variable to get the correct answer.