A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in ______.A 12 days B 13 days C days D days
Question
A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in ______.A 12 days B 13 days C days D days
Solution
First, we need to find out how much work A and B can do in a day.
- A can complete the work in 16 days, so A can do 1/16 of the work in a day.
- B can complete the work in 12 days, so B can do 1/12 of the work in a day.
Next, we need to find out how much work they can do together in two days (since they are working on alternate days starting with A).
- In two days, A and B can do (1/16 + 1/12) of the work.
- Simplifying this, we get (3/48 + 4/48) = 7/48 of the work in two days.
Now, we need to find out how many two-day intervals are needed to complete the work.
- The total work is 1 (as it's the whole), so we divide 1 by 7/48 to get the number of two-day intervals.
- This gives us approximately 6.857 two-day intervals.
Since we can't have a fraction of a day, we round this up to 7 two-day intervals, which is 14 days.
However, since they start with A and A works on the first day of each two-day interval, A will have worked an extra day by the end of the 7th interval. So, we subtract one day from the total.
Therefore, the total work will be completed in 14 - 1 = 13 days.
So, the answer is B) 13 days.
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