X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Choose one: A) 6 days B) 10 days C) 15 days D) 16 days E) 20 days

Rationale: work done by x in 4 days = ( 1 / 20 ) * 4 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 . ( x + y ) ' s 1 day ' s work = 1 / 20 + 1 / 12 = 8 / 60 = 2 / 15 . now , 2 / 15 work is done by x and y in 1 day . so , 4 / 5 work will be done by x and y in ( 15 / 2 x 4 / 5 ) = 6 days . hence , total time taken = ( 6 + 4 ) days = 10 days . option b
Answer: B