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Question

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(a) 220 km

(b) 224 km

(c) 230 km

(d) 234 km

Answer
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Let us assume that the total distance a man travelled in a journey is x km.

Now, it is given that the man travelled half of the distance i.e. $\dfrac{x}{2}$ with a speed of 21 km/hr. Then the time taken by the man to travel $\dfrac{x}{2}$ is going to be calculated by using the following formula:

$Speed=\dfrac{\text{Distance}}{\text{Time}}$

Substituting distance as $\dfrac{x}{2}$ and speed as 21 in the above formula we get,

$\begin{align}

& 21=\dfrac{\dfrac{x}{2}}{\text{Time}} \\

& \Rightarrow Time=\dfrac{x}{2\left( 21 \right)}=\dfrac{x}{42} \\

\end{align}$

This is the time that a man took in travelling the first half of the journey.

Now, we are going to calculate the time taken by a man to travel the other half of the journey with a speed of 24 km/hr.

$Speed=\dfrac{\text{Distance}}{\text{Time}}$

Substituting distance as $\dfrac{x}{2}$ and speed as 24 in the above formula we get,

$\begin{align}

& 24=\dfrac{\dfrac{x}{2}}{\text{Time}} \\

& \Rightarrow Time=\dfrac{x}{2\left( 24 \right)}=\dfrac{x}{48} \\

\end{align}$

It is given that the total time taken by a man to cover the total journey is 10 hours so adding the time of the two halves of the journey and adding them to 10.

$\begin{align}

& \dfrac{x}{42}+\dfrac{x}{48}=10 \\

& \Rightarrow x\left( \dfrac{8+7}{336} \right)=10 \\

& \Rightarrow x\left( \dfrac{15}{336} \right)=10 \\

& \Rightarrow x=\dfrac{10\times 336}{15}=224 \\

\end{align}$

Hence, the distance of the journey is equal to 224 km.

For instance in the below formula,

$Speed=\dfrac{\text{Distance}}{\text{Time}}$

If speed is in km/hr, then units of distance should be in km and time should be in hour.

Luckily in this problem, time, distance and speed are already given in such a way that they are in sync with the above formula. But in other questions, you won’t be that lucky and might be time is given in minutes and speed is in km/hr and distance is in km then you have to convert time in hr to make the speed, distance and time sync with each other.

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