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Tarun can cover a certain distance in 1hr 24min by covering $\dfrac{2}{3}$ of the distance at 4km/hr and the rest at 5km/hr. The total distance is:
A. 5km
B. 6km
C. 8km
D. 9.2km

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Last updated date: 24th Feb 2024
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IVSAT 2024
Answer
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Hint: For solving this question you should know about the general relationship of speed and time and distance. In this problem we will use the general formula for the time, which is equal to the ratio of the distance with speed. This is known as the speed-distance relation. We will calculate the time for both and then we will calculate the total distance with the help of this.

Complete step-by-step solution:
According to our question it is given that Tarun can cover a certain distance in 1hr 24min by covering $\dfrac{2}{3}$ of the distance at 4km/hr and the rest at 5km/hr. So, we have to calculate the total distance for this. As we know that the speed of anything depends on it’s motion. And if speed increases, then the time decreases and if the speed decreases, then the time increases. This means both are dependent on each other. And these are both dependent on each other as: $\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}$. The distance is always the same for any two points, so the varying parameters are only time and speed.
So, let the total distance be $S \text{km}$.
Total time = $1\text{hr}24\min = 1hr+\dfrac{24}{60}= \dfrac{21}{15} hr $.
Tarun covers $\dfrac{2}{3}$ of the distance at 4km/hr,
So, the time to cover this distance = $\dfrac{\dfrac{2}{3}S}{4}$
So, the remaining distance = $S-\dfrac{2}{3}S=\dfrac{1}{3}S$.
Tarun covers the rest of the distance at 5km/hr,
So, the time to cover the rest of the distance = $\dfrac{\dfrac{1}{3}S}{5}$.
$\begin{align}
  & \therefore \dfrac{21}{15}=\dfrac{2S}{12}+\dfrac{S}{15} \\
 & \Rightarrow \dfrac{21}{15}=\dfrac{14S}{60} \\
 & \Rightarrow S=\dfrac{21\times 60}{14\times 15}=6\text{km} \\
\end{align}$
So, the total distance is 6km.
Hence option B is the correct answer.

Note: While solving these types of questions you have to keep in mind that we will strictly use the relationship of time, distance and speed to solve these questions. If we will not use it, then it is not possible to find our required answer.