Raman covers 1 km in 8 minutes, while Suman covers 1 km in 10 minutes. In a 1 km race finished by Raman, by what distance does Raman beat Suman?

Introduction / Context:In head-to-head races, compare distances covered in the winner's finishing time to find the margin (lead) in meters.

Given Data / Assumptions:

• Raman's time for 1 km = 8 minutes ⇒ speed = 1000/8 = 125 m/min.
• Suman's time for 1 km = 10 minutes ⇒ speed = 1000/10 = 100 m/min.
• Race ends when Raman completes 1000 m (8 minutes).

Concept / Approach:Lead = Raman's finish distance minus Suman's distance at the same time. Since Suman runs at 100 m/min, in 8 minutes he covers 800 m.

Step-by-Step Solution: Suman's distance at Raman's finish = 100 m/min * 8 min = 800 m Lead = 1000 - 800 = 200 m

Verification / Alternative check:Speed ratio 125:100 = 5:4; over 1000 m, the expected lead is (1 - 4/5) * 1000 = 200 m. Matches.

Why Other Options Are Wrong:150, 65, 190 m do not match the computed lead using consistent speeds; the calculation is exact.

Common Pitfalls:Comparing finish times rather than distances at a fixed time; mixing minutes and seconds; using average of speeds incorrectly.

Final Answer:200 m