Given the task definition and input, reply with output. In this task, you need to answer the given multiple-choice question on the physics. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: two fill taps a and b can separately fill a cistern in 45 and 40 minutes respectively . they started to fill a cistern together but tap a is turned off after few minutes and tap b fills the rest part of cistern in 23 minutes . after how many minutes , was tap a turned - off ?
Options: a ) 9 min , b ) 10 min , c ) 12 min , d ) 7 min , e ) none of these
a