SOLUTION:

Result of A:B and B:C races means A:C = 400:208.

So, as we're dealing with integers, jars must contain a

multiple of 25, since 25:13 is lowest.

There are 13 such possibilities in the 200-500 range:

Code:

A ate C ate A-C SUMDIGITS
200 104 96 15
225 117 108 9
250 130 120 3***
275 143 132 6
300 156 144 9
325 169 156 12
350 182 168 15
375 195 180 9
400 208 192 12
425 221 204 6
450 234 216 9
475 247 228 12
500 260 240 6

***Only 3 is unique as sum of digits of the differences.

If Jack had pointed to any of other numbers, John could not have known.

So N = 250.