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: 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
a

Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 3, – 4 ), k = ( – 3, 1 ), l = ( 5, 7 ), and m = ( 5, – 4 ). what is its perimeter ?
Options: a. 34, b. 36, c. 38, d. 40, e. ( f ) 42
a

Problem: two trains, one from howrah to patna and the other from patna to howrah, start simultaneously. after they meet, the trains reach their destinations after 32 hours and 16 hours respectively. the ratio of their speeds is
Options: a. 4: 9, b. 4: 3, c. 4: 12, d. 1: 2, e. 4: 5

d