A can do a piece of work in 2 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?  Choose the most appropriate option
A) 12
B) 9
C) 8
D) 6
E) 3

Rationale: "a ' s 1 hour ' s work = 1 / 2 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 2 + 1 / 3 ) = 5 / 6 . b ' s 1 hour ' s work = ( 5 / 6 - 1 / 2 ) = 1 / 3 . therefore a alone will take 3 hours to do the work . e"
Answer: E