In a 200 m race, runner A can beat B by 31 m and beat C by 18 m. In a 350 m race, by how many metres will C beat B?

Introduction / Context:
This problem combines two separate race results to compare the speeds of runners B and C. It appears in aptitude tests to check if a student can translate statements like A beating B by a certain distance into speed ratios and then reuse those ratios for a new race distance between different runners.

Given Data / Assumptions:
- In a 200 m race, when A finishes 200 m, B has covered only 169 m. - In the same 200 m race, when A finishes 200 m, C has covered 182 m. - Speeds of A, B, and C remain constant across races. - We must find how many metres C will beat B by in a 350 m race.

Concept / Approach:
The key idea is that distances covered in the same time are proportional to speeds. From the first race we can find the ratio of speeds vB and vC relative to vA. Then we divide these ratios to get the direct ratio vB : vC. Finally, we apply this ratio to a new race where C runs 350 m, and we calculate B's distance at the same time to find the lead of C.

Step-by-Step Solution:
Step 1: In 200 m race, A vs B gives vB / vA = 169 / 200. Step 2: From the same race, A vs C gives vC / vA = 182 / 200. Step 3: Ratio of speeds B to C is vB / vC = (169 / 200) / (182 / 200) = 169 / 182. Step 4: In a new race, let C run the full 350 m. Time taken by C is proportional to 350 / vC. Step 5: In that same time, distance covered by B is 350 * (vB / vC) = 350 * 169 / 182. Step 6: Compute the gap: lead of C over B = 350 - 350 * 169 / 182. Step 7: Simplify: 350 * (1 - 169 / 182) = 350 * (13 / 182) = 25 m.

Verification / Alternative check:
We can scale speeds directly. Take vB = 169 units and vC = 182 units. If C covers 350 m, the time factor is proportional to 350 / 182. In that time B would cover (169 / 182) * 350 = 325 m. The difference 350 - 325 again equals 25 m, confirming the previous calculation and ensuring that there is no arithmetic mistake.

Why Other Options Are Wrong:
- 22.75 m and 19.5 m: These values arise if incorrect ratios are used or if distances are subtracted before forming speed ratios. - 18.5 m: This is smaller than the correct difference and does not match the exact fractional computation.

Common Pitfalls:
A frequent mistake is to subtract gaps directly, for example by manipulating 31 m and 18 m without converting them into speed ratios. Another error is reversing the ratio, using vC / vB instead of vB / vC at the wrong stage. Always express speeds in terms of one runner (here A), then divide to get vB : vC cleanly, and only then apply this ratio to the new race distance.

Final Answer:
In a 350 m race, C will beat B by 25 m.