Given the task definition and input, reply with output. 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.

Problem: the ratio of investments of two partners p and q is 7: 5 and the ratio of their profits is 7: 11. if p invested the money for 5 months, find for how much time did q invest the money ?
Options: a. 19, b. 17, c. 13, d. 11, e. 12
d