In a 50 m race, A can give a start of 5 m to B and a start of 14 m to C. In the same race, how much start can B give to C?

To solve this problem, we need to understand the concept of "giving a start" in a race. When we say "A can give a start of 5 m to B", it means that A is fast enough to finish the race even if B starts 5 m ahead. Similarly, "A can give a start of 14 m to C" means A can finish the race even if C starts 14 m ahead.

1. First, let's find out the relative speeds of A, B, and C. If A can give B a 5 m start in a 50 m race, it means A runs 50 m while B runs 45 m. So, the ratio of their speeds is 50:45 or 10:9 (A:B).

2. Similarly, if A can give C a 14 m start, it means A runs 50 m while C runs 36 m. So, the ratio of their speeds is 50:36 or 25:18 (A:C).

3. Now, we need to find out how much start B can give to C. For this, we need to find the ratio of B's speed to C's speed. We know the ratios of A:B and A:C, so we can use these to find B:C.

   The ratio of B's speed to C's speed is (B/A) / (C/A) = (B/C). Substituting the values we have, (10/9) / (25/18) = (10/9) * (18/25) = 8/5.

4. So, the ratio of B's speed to C's speed is 8:5. This means that when B runs 8 m, C runs 5 m.

5. In a 50 m race, when B runs the full distance, C would run (50/8)*5 = 31.25 m.

6. Therefore, B can give C a start of 50 - 31.25 = 18.75 m in a 50 m race.