In a 1000 m race, Arjun, Balaji and Charan are running. Arjun beats Balaji by 100 m, and Balaji beats Charan by 100 m. In the next 1000 m race (the speeds are the same as in the previous), Balaji gives Charan ahead start of 100 m, and Arjun gives Balaji ahead start of 100 m. Find the distance by which the winner is ahead of the person just behind him.

Given:

In a 1000 m race, Arjun, Balaji, and Charan are running. Arjun beats Balaji by 100 m, and Balaji beats Charan by 100 m.

In the next 1000 m race (the speeds are the same as in the previous), Balaji gives Charan an ahead start of 100 m, and Arjun gives Balaji an ahead start of 100 m.

Concept used:

Distance = Speed × Time

Calculation:

In a 1000 m race, Arjun beats Balaji by 100 m.

Hence, while Arjun covers 1000 m, Bajali covers 900 m.

So, Speed (Arjun) : Speed (Balaji) = 1000 : 900 = 10 : 9 = 100 : 90

In a 1000 m race, Balaji beats Charan by 100 m.

Hence, while Balaji covers 1000 m, Charan covers 900 m.

So, Speed (Balaji) : Speed (Charan) = 1000 : 900 = 10 : 9 = 90 : 81

Hence, Speed (Arjun) :Speed (Balaji) : Speed (Charan) = 100 : 90 : 81

Let the speed of Arjun, Balaji and Charan be 100k, 90k and 81k respectively.

In the next race,

Arjun has to cover = 1000 m

Balaji has to cover = 1000 - 100 = 900 cm

Charan has to cover = 900 - 100 m = 800 m

In the next race,

Time taken by Arjun to reach the finish line = 1000/100k = 10/k

Time taken by Balaji to reach the finish line = 900/90k = 10/k

Time taken by Charan to reach the finish line = 800/81k ≈ 9.8/k

Considering the fractions, we can clearly see that the winner will be Charan.

By that time,

Arjun will cover = 100k × 9.8/k ≈ 980 m

Balaji will cover = 90k × 9.8/k ≈ 880 m

Now, the distance by which the winner is ahead of the person just behind him = 1000 - 980 = 20m

∴ The distance by which the winner is ahead of the person just behind him is 20 m.