To complete a work A and B takes 8 days, B and C takes 12 days, A,B and C takes 6 days. How much
time A and C will take  Choose the correct answer.
A) 24 days  B) 16 days  C) 12 days  D) 8 days  E) none of these

Rationale: explanation : a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + b + c 1 day work = 1 / 6 we can get a work by ( a + b + c ) - ( b + c ) and c by ( a + b + c ) - ( a + b ) so a 1 day work = 1 / 6 − 1 / 12 = 1 / 12 similarly c 1 day work = 1 / 6 − 1 / 8 = 4 − 3 / 24 = 1 / 24 so a and c 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 so a and c can together do this work in 8 days option d
Answer: D