A 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?Options7 5/9 days8 days9 days14 2/5 days
Question
A 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?Options7 5/9 days8 days9 days14 2/5 days
Solution
To solve this problem, we need to first understand the work rate of A and B.
- 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, the amount of work done by B alone is 17 * (1/35) = 17/35 of the work.
Since the total work is 1, the work done by A and B together before A left is 1 - 17/35 = 18/35 of the work.
Let's denote the number of days A worked as x. So, the equation based on the work done by A and B together is:
x * (9/140) = 18/35
Solving this equation for x gives us:
x = (18/35) * (140/9) = 56/9 = 6 2/9 days.
So, A worked for approximately 6 2/9 days before leaving. However, this option is not available in the given options. There might be a mistake in the problem or the options.
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