Spelling B

Alice, Betty, and Carol took the same series of examinations. There was one grade of A, one grade of B, and one grade of C for each examination, where A, B, C are different positive integers. The final test scores were

Alice: 20
Betty: 10
Carol: 9

If Betty placed first in the arithmetic examination, who placed second in the spelling examination?

(Assume that no two students got the same grade in same examination.)

The puzzle appeared in the 16th International Mathematical Olympiad, Erfurt-Berlin, July 1974.

Solution