Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

[EX Q]: Problem: a and b invests rs. 8000 and rs. 12000 in a business. after 4 months, a withdraws half of his capital and 2 months later, b withdraws one - third of his capital. in what ratio should they share the profits at the end of the year ?
Options: a. 32: 99, b. 82: 31, c. 8: 15, d. 34: 89, e. 35: 21
[EX A]: c

[EX Q]: Problem: a cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour. what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a. 8.1, b. 8.9, c. 8.6, d. 8.3, e. 9.0
[EX A]: b

[EX Q]: Problem: a student travels from his house to school at 10 km / hr and reaches school 2 hours late. the next day he travels 15 km / hr and reaches school 1 hour early. what is the distance between his house and the school ?
Options: a. 60, b. 70, c. 80, d. 90, e. 100
[EX A]:
d