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.

Input: Consider Input: Problem: raman mixed 48 kg of butter at rs. 150 per kg with 36 kg butter at the rate of rs. 125 per kg. at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a. 129, b. 287, c. 195, d. 188, e. 112

Output: c

Input: Consider Input: Problem: if p ( a. = 5 / 7 and p ( b. = 2 / 5, find p ( a n b. if a and b are independent events.
Options: a. 7 / 25, b. 3 / 25, c. 8 / 25, d. 2 / 7, e. 3 / 17

Output: d

Input: Consider Input: Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability q that this product will be a multiple of 45 ?
Options: a. 1 / 32, b. 1 / 28, c. 1 / 24, d. 1 / 16, e. 1 / 14
Output: c