In a running race, when one runner allows another runner to stay ahead at the start of the race, then it is termed as startup and when runners reach the finishing line at the same time, then it is termed as dead heat. In a race of 4 km distance, Anu wins by 600m over Binu. Binu can give a startup of 200m to Caira in a 4 km race. By how much distance should Caira get startup so that the race between Anu and Caira ends in dead heat in the same race of 4 km?

Let Anu finishes the race in t hours.

Speed of Anu = $$\ \frac{\ 4000}{t}$$ m/hour

Speed of Bhanu = $$\ \frac{\ \left(4000-600\right)}{t}$$ m/hour Since Anu wins the race by 600m

Time taken by Bhanu to finish the race = Time taken by Caira to cover 3800m.

Time taken by Bhanu = $$\ \frac{\ 4000}{\ \frac{\ 3400}{t}}\ =\ \ \frac{\ 20}{17}t$$

Speed of Caira = $$\ \frac{\ 3800}{\ \frac{\ 20}{17t}}\ =\ \ \frac{\ 3230}{t}$$ m.hr.

To finish the race at the same time Anu should give Caira a headstart of 4000-3230 = 770m

C is the correct answer.