A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/5rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?  Choose the correct choice from the following.
A) 1/3 B) 2/9 C) 9/49 D) 25/129 E) 1/6
The first thing to notice is that A is faster than B and B is faster than C.   Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.   If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.   Therefore total work done = (2*2) + (1*1) + (2/5*2/5) = 129/25   Proportion of work done by B = (1*1) / (129/25) =25/129   Hence Answer 25/129.
<result>D</result>
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/5rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?