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.

Example Input: Problem: for 2 consecutive yrs, my incomes are in the ratio of 4: 7 and expenses in the ratio of 3: 5. if my income in the 2 nd yr is rs. 42000 & my expenses in the first yr in rs. 23000, my total savings for the two - year is
Options: a. s. 8000, b. s. 9000, c. s. 9900, d. s. 9990, e. s. 10000
Example Output: a

Example Input: Problem: arjun started a business with rs. 20,000 and is joined afterwards by anoop with rs. 30, 000. after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a. 3, b. 4, c. 5, d. 6, e. 7
Example Output: b

Example Input: Problem: for all numbers a and b, the operation is defined by ab = ( a + 2 ) ( b – 3 ). if 3 x = – 20, then x =
Options: a. – 15, b. – 6, c. 3, d. 6, e. - 1
Example Output:
e