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Arun and Barun are both athletes. However, Arun runs $25\%$ faster than Barun. He is able to allow Barun a lead of $7$ meters to end a race in scorching heat. What is the length of the race ?

1. $10$ meters
2. $25$ meters
3. $15$ meters
4. $35$ meters

Option D. 35 meters

Method 1

Say Barun speed is 1 m/s
then Arun speed would be 1.25 m/s
also, say length of the race is x meters
Time taken by both the player would be same
i.e. [time taken by Arun]$\frac{x}{1.25}$ = $\frac{x-7}{1}$ [time taken by Barun]

by solving this equation x = 35 meters

Method 2

Arun runs 25% as fast as Barun.
i.e., if Barun runs 100 m in a given time, Arun will run 125 m in the same time.
In other words, if Arun runs 5 m in a given time, then Barun will run 4 m in the same time.

Therefore, if the length of a race is 5 m, then Arun can give Barun a start of 1 m (Arun can allow Barun to start 1 ahead of the starting point) so that they finish the race in a scorching heat.
Ratio of length of start given : length of race :: 1 : 5

In this question, we know that the start given is 7 m.
Hence, the length of the race will be 7 * 5 = 35 meters.

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$\frac{25}{100}*x = 7$   [25% faster Arun covers extra 7 meters]

So, x = 28

Arun takes a lead of 7 meters, so length of the race = 28 + 7 = 35 meters

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