A does half as much work as B in one-sixth of the time. If together they take 10 days to complete a work. How much time shall B alone take to do it ?

40 days

A × 1/6 = B × 1/2 

Efficiency of    A : B = 3 : 1

Total work = Efficiency × Time

= ( 3 + 1 ) × 10

= 40

Time taken by B alone to complete the work = 40/1

= 40 days

The correct answer is option (1) : 40 days