In a 200 meter race, runner A can beat runner B by 31 meters and runner C by 18 meters. If there is a 350 meter race between C and B alone, by how many meters will C beat B?

Introduction / Context:
This is a standard athletics style aptitude question involving races and relative speeds. When one runner beats another by a certain distance in the same time, their speeds are in the ratio of the distances each covers. The problem then asks you to use this ratio to predict the outcome for a different race distance between two of the runners.

Given Data / Assumptions:

• Race distance in the first case = 200 meters.
• When A finishes 200 meters, B has covered 200 - 31 = 169 meters.
• When A finishes 200 meters, C has covered 200 - 18 = 182 meters.
• The speeds of A, B, and C are proportional to the distances they cover in the same time.
• We need to compare C and B in a new race of 350 meters.

Concept / Approach:
Because A, B, and C run for the same time in the reference 200 meter race, their speeds are directly proportional to the distances they each cover in that time. Therefore, the speed ratio A:B:C is 200:169:182. For the second race, only C and B are running, and they keep these same speeds. Using the speed ratio for C and B, we calculate how far B has run when C finishes 350 meters, then subtract to find the lead of C over B.

Step-by-Step Solution:
Speed of B is proportional to 169 units, and speed of C is proportional to 182 units. Speed ratio B:C = 169:182. In the new race, C covers 350 meters. Let distance covered by B when C finishes 350 meters be d meters. Because speeds are proportional, d / 350 = 169 / 182. So d = 350 * 169 / 182. Compute d = (350 * 169) / 182 = 325 / ? we simplify numerically. 350 * 169 = 59150 and 59150 / 182 = 325 meters. Lead of C over B = 350 - d = 350 - 325 = 25 meters.

Verification / Alternative check:
We can cross check the arithmetic by noting that 182 is close to 200 and 169 is significantly smaller, making C clearly faster than B. For a longer race, C should pull further ahead. A quick approximate ratio 169 / 182 is slightly less than 0.93. Multiplying 350 by about 0.93 gives approximately 325 meters for B, leaving about 25 meters difference, which matches the exact calculation.

Why Other Options Are Wrong:
Differences of 21 meters, 22 meters, and 19 meters underestimate the lead that C will achieve over a 350 meter race given the significant speed difference implied by the original race. A difference of 28 meters is slightly larger than the correct value and does not match the precise proportional calculation. Only 25 meters accurately follows from the exact ratio of the speeds.

Common Pitfalls:
Students sometimes confuse the distances by which A beats B and C with the distances between B and C directly. Others try to scale up the given leads without using ratios, which leads to incorrect answers. The safe method is always to convert performance in one race into a speed ratio, then apply that ratio to the new race distance to find the finish positions.

Final Answer:
In the 350 meter race, runner C will beat runner B by 25 m.