In a 1000 m race, Arjun, Balaji and Charan are running. Arjun beats Balaji by 100m, 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 a head start of 100 m, and Arjun gives Balaji a head start of 100m. Find the distance by which the winner is ahead of the person just behind him.
Answer & explanation
Correct answer: option 4
In a 1000 m race, Arjun beats Balaji by 100m
ratio of Arjun : Balaji
Distance 1000 : 900
Speed 10 : 9
In a 1000 m race, Balaji beats Charan by 100 m
ratio of Balaji : Charan
Distance 1000 : 900
Speed 10 : 9
Overall, Speed of Arjun : Balaji : Charan = 100 : 90 : 81
In the next race,
Distance covered by Arjun = 1000 m
Time taken by Arjun to cover 1000m = \(\frac{1000}{100R}\) = \(\frac{10}{R}\)
Distance covered by Balaji = 900 m
Time taken by Balaji to cover 900m = \(\frac{900}{90R}\) = \(\frac{10}{R}\)
Distance covered by Charan = 800 m
Time taken by Charan to cover 800m = \(\frac{800}{90R}\) = \(\frac{9.8}{R}\)
Charan takes least time and winner of race.
Distance covered by Arjun in \(\frac{9.8}{R}\) sec = 100R x \(\frac{9.8}{R}\)
= 980 m
Distance covered by Balaji in \(\frac{9.8}{R}\) sec = 90R x \(\frac{9.8}{R}\)
= 880 m
Now, the distance by which the winner is ahead of the person just behind him
= 1000 - 980
= 20 m