A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.a.3 ½ daysb.2 daysc.1 ½ daysd.3 days
Question
A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.a.3 ½ daysb.2 daysc.1 ½ daysd.3 days
Solution
To solve this problem, we first need to find out how much work A and B can do in one day, which is their work rate.
- A's work rate is 1 work per 6 2/3 days, or 1/(20/3) = 3/20 of the work per day.
- B's work rate is 1 work per 5 days, or 1/5 of the work per day.
When they work together, their combined work rate is the sum of their individual work rates.
- Combined work rate = A's work rate + B's work rate = 3/20 + 1/5 = 7/20 of the work per day.
They work together for 2 days, so the amount of work they complete is:
- Work completed = Combined work rate * time = 7/20 * 2 = 7/10 of the work.
This means there is 1 - 7/10 = 3/10 of the work left to be done.
Finally, we need to find out how long it will take B to complete the remaining work alone. We do this by dividing the remaining work by B's work rate:
- Time = Remaining work / B's work rate = 3/10 / 1/5 = 1.5 days.
So, the answer is c. 1 ½ days.
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