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.
--------
Question: 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

Answer: d


Question: Problem: two taps a and b can fill a cistern in 12 minutes and 18 minutes respectively. they are turned on at the same time. if the tap a is turned off after 4 minutes, how long will tap b take to fill the rest of the cistern ?
Options: a. 8 min., b. 9 min., c. 10 min., d. 7 min., e. none of these

Answer: a


Question: Problem: tough and tricky questions: ratios 4 / 5 of a certain class left on a field trip. 1 / 3 of the students who stayed behind did not want to go on the field trip ( all the others did want to go ). when another vehicle was located, 1 / 2 of the students who did want to go on the field trip but had been left behind were able to join. what fraction of the class ended up going on the field trip ?
Options: a. 1 / 2, b. 2 / 3, c. 13 / 15, d. 23 / 30, e. 4 / 5

Answer:
c