Question

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?

• A. 700m
• B. 750m
• C. 770m
• D. 725m

Answer 1

The Correct Option is C

Step 1: Chain the two ratios.
Anu to Binu is \( 4000 : 3400 = 20 : 17 \), and Binu to Caira is \( 4000 : 3800 = 20 : 19 \). So Anu to Caira is \( \frac{20}{17} \times \frac{20}{19} = \frac{400}{323} \).

Step 2: Scale this onto 4000 m.
When Anu covers 400 parts, Caira covers 323 parts, and each part here is \( \frac{4000}{400} = 10 \) m. So Caira covers \( 323 \times 10 = 3230 \) m.

Step 3: Find the startup needed.
Caira needs a head start of \( 4000 - 3230 = 770 \) m. \[ \boxed{770 \text{ m}} \]