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Aman travels a certain distance at x km/h. In the return journey, he covers 20% of the same distance in 35% of the time taken to cover the earlier distance. For the remaining part of the return journey, if his speed is y km/h, and he can cover the entire return journey in the same time as for the onward journey, then which of the following is true? 

Aman travels a certain distance at x km/h. In the return journey, he covers 20% of the same distance in 35% of the time taken to cover the earlier distance. For the remaining part of the return journey, if his speed is y km/h, and he can cover the entire return journey in the same time as for the onward journey, then which of the following is true?  Correct Answer 13y = 16x

Given:

Aman travels a certain distance at x kmph.

In the return journey, he covers 20% of the same distance in 35% of the time taken to cover the earlier distance.

For the remaining part of the return journey, if his speed is y km/h, and he can cover the entire return journey in the same time as for the onward journey.

Formula used:

Distance = Speed × Time

Calculation:

Let the time of travel for the onward journey = 10 hours

The speed of Aman for onward journey = x kmph

The distance travelled by Aman = 10x km

Now, 

In case of return journey:

In the first part:

The 20% of the distance = 20% of 10x = 2x km

The time required to cover the 20% of the journey = 35% of 10 = 3.5 hours

For the remaining part of the return journey:

The speed of Aman = y kmph

The time required to travel the remaining distance = 10 - 3.5 = 6.5 hours

The distance travelled = 6.5y km

Since the distance of travelled is same in both case are same,

Therefore,

⇒ 10x = 2x + 6.5y

⇒ 8x = 6.5y

⇒ 16x = 13y

∴ 13y = 16x is the required relation.

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