Pankaj walked at 5 km/h for certain part of the journey and then he took an auto for the remaining part of the journey travelling at 25 km/h. He took 10 hours for the entire journey. What part of the journey did he travel by auto if the average speed of the entire journey be 17 km/h:a)750 kmb)100 kmc)150 kmd)200 kme)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Let's assume that the distance traveled by Pankaj by auto is 'd' km.

To find the part of the journey traveled by auto, we need to find the ratio of the distance traveled by auto to the total distance.

Let's assume the total distance of the journey is 'x' km.

We know that Pankaj walked at a speed of 5 km/h for a certain part of the journey. So, the time taken for this part of the journey can be calculated as 't1 = (x - d) / 5' hours.

We also know that Pankaj took an auto for the remaining part of the journey and traveled at a speed of 25 km/h. So, the time taken for this part of the journey can be calculated as 't2 = d / 25' hours.

The total time taken for the entire journey is given as 10 hours. So, we can write the equation as:

t1 + t2 = 10

Substituting the values of t1 and t2, we get:

(x - d) / 5 + d / 25 = 10

Simplifying the equation, we get:

(5(x - d) + d) / 25 = 10

Multiplying both sides of the equation by 25, we get:

5(x - d) + d = 250

Expanding the equation, we get:

5x - 5d + d = 250

Simplifying the equation, we get:

5x - 4d = 250

Now, we also know that the average speed of the entire journey is 17 km/h. The average speed is calculated as the total distance divided by the total time taken. So, we can write another equation as:

x / 10 = 17

Multiplying both sides of the equation by 10, we get:

x = 170

Substituting the value of x in the equation 5x - 4d = 250, we get:

5(170) - 4d = 250

850 - 4d = 250

Subtracting 850 from both sides of the equation, we get:

-4d = -600

Dividing both sides of the equation by -4, we get:

d = 150

Therefore, Pankaj traveled 150 km by auto.

Hence, the correct answer is option C) 150 km.

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