A does half as much work as B in one-sixth of the time. If together they take 10 days to complete a piece of work, how much time shall B alone take to do it?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 40 days
Compare the rates of work first. If A does half of B's work in one-sixth of B's time, then in B's full time A would do six such halves.
In the time B does 1 unit of work, A does \(6\times\frac{1}{2}=3\) units: A works 3 times as fast as B
Let B do 1 unit a day; then A does 3 units a day, and together they do 4 units a day
Total work = 4 units a day × 10 days = 40 units
B alone: 40 units ÷ 1 unit a day = 40 days