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

This problem requires an initial comprehension of the scenario, followed by a calculation of the result using the provided ratio and head start.

Step 1: Data Comprehension

• Race distance: 600 m
• Speed ratio (A:B): 4:5
• A's head start: 200 m

Step 2: Calculate Effective Distance for A

• With a 200 m head start, A needs to cover (600 - 200) = 400 m.

Step 3: Calculate Time for Each Participant

• Assume A's speed = 4x and B's speed = 5x.
• Time for A to cover 400 m = 400/(4x) = 100/x
• Time for B to cover 600 m = 600/(5x) = 120/x

Step 4: Determine the Outcome

• Since 100/x < 120/x, A finishes first.
• In 100/x time, B covers 5x * (100/x) = 500 m.
• Therefore, B is at 500 m when A finishes.
• A wins by a margin of 600 m (total distance for B) - 500 m (distance covered by B) = 100 m.

A wins by 100 m.