Answer : Option C

Explanation :

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Solution 1 (Quick)
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$MF#%\begin{align}
&\text{If a car covers a certain distance at x kmph and an equal distance at y kmph. Then,}\\
&\text{the average speed of the whole journey = }\dfrac{2xy}{x+y}\text{ kmph.}\\\\\\\\\\\\
&\text{By using the same formula, we can find out the average speed quickly}\\\
&\text{average speed = }\dfrac{2 \times 84 \times 56}{84 + 56} = \dfrac{2\times84 \times 56}{140} = \dfrac{2 \times 21 \times 56}{35}\\\\
&= \dfrac{2 \times 3 \times 56}{5} = \dfrac{336}{5} = 67.2
\end{align} $MF#%
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Solution 2 (Fundamentals)
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Though it is a good idea to solve the problems quickly using formulas, you should
know the fundamentals too. Let's see how we can solve this problems using basics
Train travels from A to B at 84 km per hour
Let the distance between A and B = x
$MF#%\text{Total time taken for traveling from A to B = }\dfrac{\text{distance}}{\text{speed}} = \dfrac{x}{84}
$MF#%
Train travels from B to A at 56 km per hour
$MF#%\begin{align}
&\text{Total time taken for traveling from B to A = }\dfrac{\text{distance}}{\text{speed}} = \dfrac{x}{56}\\\\\\\\\\\\\\\
&\text{Total distance travailed = }x + x = 2x\\\\
&\text{Total time taken = }\dfrac{x}{84} + \dfrac{x}{56}\\\\
&\text{Average speed = }\dfrac{\text{Total distance traveled}}{\text{Total time taken}} = \dfrac{2x}{\dfrac{x}{84} + \dfrac{x}{56}}\\\\\\\\
&= \dfrac{2}{\dfrac{1}{84} + \dfrac{1}{56}} = \dfrac{2 \times 84 \times 56}{56 + 84}= \dfrac{2\times84 \times 56}{140} = \dfrac{2 \times 21 \times 56}{35}= \dfrac{2 \times 3 \times 56}{5}\\\\
&= \dfrac{336}{5} = 67.2
\end{align} $MF#%