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 Input:
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 Output:
c


Ex Input:
Problem: if a - b = 6 and a 2 + b 2 = 50, find the value of ab.
Options: a. a. 7, b. b. 12, c. c. 15, d. d. 18, e. e. 20

Ex Output:
a


Ex Input:
Problem: if a farmer wants to plough a farm field on time, he must plough 120 hectares a day. for technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a. 600, b. 490, c. 720, d. 435, e. 679

Ex Output:

c