Select the correct answerA can complete a work in 12 days, B in 15 days. When A and B worked alternatively, when started byOptions12 2/5 days11 2/5 days13 3/5 days13 2/5 days
Question
Select the correct answerA can complete a work in 12 days, B in 15 days. When A and B worked alternatively, when started byOptions12 2/5 days11 2/5 days13 3/5 days13 2/5 days
Solution
To solve this problem, we first need to find out how much work A and B can do in a day.
- A can complete the work in 12 days, so A can do 1/12 of the work in a day.
- B can complete the work in 15 days, so B can do 1/15 of the work in a day.
When A and B work alternatively, they can complete (1/12 + 1/15) of the work in two days.
To simplify this, we find the least common multiple of 12 and 15, which is 60. So, A can do 5/60 of the work in a day and B can do 4/60 of the work in a day.
Together, they can do (5/60 + 4/60) = 9/60 = 3/20 of the work in two days.
To find out how many days they will take to complete the work, we divide the total work (1) by the work they can do in two days (3/20), which gives us 20/3 = 6 2/3.
Since they are working for two days at a time, we multiply this by 2, which gives us 13 1/3 days.
However, since A starts first, A will work on the 14th day. So, they will complete the work in 13 1/3 days if B starts first, but since A starts first, they will complete the work in 13 2/5 days.
So, the correct answer is 13 2/5 days.
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