Question

In a 600 m race, the ratio of the speeds of two participants A and B is 4:5. If A has a head start of 200 m, then the distance by which A wins is:

• A. 500 m
• B. 200 m
• C. 100 m
• D. 120 m

Answer 1

The Correct Option is C

To solve this problem, we will first understand the given situation and then calculate the outcome using the given ratio and head start distance.

Step 1: Understanding the Given Data

• Distance of the race = 600 m
• Speed ratio of A to B = 4:5
• Head start for A = 200 m

Step 2: Calculate the Effective Distance

• Since A gets a head start of 200 m, A only needs to cover (600 - 200) = 400 m to finish the race.

Step 3: Calculate the Time Taken by Each Participant

• Let's assume the speed of A = 4x and speed of B = 5x.
• Time taken by A to cover 400 m = Distance/Speed = 400/(4x) = 100/x
• Time taken by B to cover 600 m = Distance/Speed = 600/(5x) = 120/x

Step 4: Determine the Outcome

• Since 100/x < 120/x, A finishes the race before B.
• In 100/x time, B would have covered 5x * (100/x) = 500 m.
• Therefore, when A finishes, B is at 500 m.
• The distance by which A wins = Total distance for B - Distance covered by B = 600 - 500 = 100 m.

Thus, the distance by which A wins is 100 m.

Answer 2

Let the speeds of A and B be \(4x\) and \(5x\), respectively. A has a head start of 200 m, so B needs to cover 600 m while A runs 400 m.

The time taken by B to finish the race is:

\[ t_B = \frac{\text{Distance by B}}{\text{Speed of B}} = \frac{600}{5x}. \]

The distance covered by A in this time is:

\[ \text{Distance by A} = \text{Speed of A} \times \text{Time taken by B} = 4x \times \frac{600}{5x} = 480 \text{ m}. \]

Thus, A finishes 480 m while B finishes the race (600 m). The distance by which A wins is:

\[ 600 - 480 = 100 \text{ m}. \]

Thus, the distance by which A wins is 100 m.