Select the correct answerA and B can do a piece of work in 28 and 35 days respectively. They began to work together but A leaves after some time and B completed the remaining work in 17 days. After how many days did A leave?Options8 days7 5/9 days9 days14 2/5 days
Question
Select the correct answerA and B can do a piece of work in 28 and 35 days respectively. They began to work together but A leaves after some time and B completed the remaining work in 17 days. After how many days did A leave?Options8 days7 5/9 days9 days14 2/5 days
Solution
To solve this problem, we first need to find the rate at which A and B work.
- A can complete the work in 28 days, so A's work rate is 1/28 work/day.
- B can complete the work in 35 days, so B's work rate is 1/35 work/day.
When they work together, their combined work rate is 1/28 + 1/35 = 9/140 work/day.
Given that B alone completed the remaining work in 17 days, we can find out how much work was left after A left. B's work rate is 1/35, so in 17 days, B completes 17/35 = 0.486 (or 48.6%) of the work.
This means that when A left, 1 - 0.486 = 0.514 (or 51.4%) of the work had already been completed.
We know that A and B together have a work rate of 9/140. So, to find out how long they worked together to complete 51.4% of the work, we divide 0.514 by their combined work rate: 0.514 / (9/140) = 7.98 days.
So, A left after approximately 8 days. Therefore, the correct answer is "8 days".
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