In an 800 m race, the ratio of the speeds of two contestants Ankur and Neha is 5 : 6. If Ankur has a head-start of 200 m, then Ankur will win by ________.

Correct Answer: 80 m

To find out by how much distance Ankur wins the race, let us analyze the total race distance, head-start, and the speeds of both contestants step-by-step.

Step 1: Determine the distance each contestant needs to run.

The total length of the race is 800 m.

Ankur has a head-start of 200 m, which means Ankur starts 200 m ahead of Neha.

Therefore, the distance Ankur needs to cover to complete the race is:

$\text{Distance for Ankur}=800-200=600\text{ m}$

Neha starts from the starting line, so the distance Neha needs to cover to complete the entire race is:

$\text{Distance for Neha}=800\text{ m}$

Step 2: Calculate the time taken by Ankur to finish his race.

The ratio of the speeds of Ankur and Neha is given as 5 : 6.

Let the speed of Ankur be $5v$ and the speed of Neha be $6v$.

The time taken by Ankur to cover his remaining distance of 600 m is:

$T_{\text{Ankur}}=\frac{600}{5v}=\frac{120}{v}$

Step 3: Calculate the distance Neha covers in the same time.

In the time $T_{\text{Ankur}}$ that Ankur takes to reach the finish line, the distance covered by Neha is:

$\text{Distance covered by Neha}=\text{Speed of Neha}\times T_{\text{Ankur}}$

$\text{Distance covered by Neha}=6v\times \frac{120}{v}=720\text{ m}$

Step 4: Find the winning distance.

When Ankur finishes the race (covering his 600 m), Neha has covered 720 m out of the total 800 m.

The remaining distance Neha still needs to run to finish the race is:

$\text{Winning distance}=800-720=80\text{ m}$

Thus, Ankur will win the race by 80 m.