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1. A group of 12 men can do a piece of work in 14 days and other group of 12 women can do the same work in 21 days. They begin together but 3 days before the completion of work, man's group leaves off. The total number of days to complete the work is:
Given,
12 men and 12 women can complete a work separately in 14 days and 21 days respectively
Then,
12 men's 1 day work =
And,
12 women's 1 day work =
Then ,
12 women's 3 days work = =
The remaining work = =
Man's group leaves 3 days before the completion of work
That is, they were working together for x - 3 days
Thus, we have work left to be done in last 3 days by the women's group. This also means th of work has been done by both the groups (before men left)
Now, (12 men + 12 women)'s 1 day work = =
i.e., work is done by 2 groups in 1 day.
So, of work is done by 2 groups together in = days
Total time take to complete the work will be
= + 3 =
Solution:
Let x be the required number of daysGiven,
12 men and 12 women can complete a work separately in 14 days and 21 days respectively
Then,
12 men's 1 day work =
And,
12 women's 1 day work =
Then ,
12 women's 3 days work = =
The remaining work = =
Man's group leaves 3 days before the completion of work
That is, they were working together for x - 3 days
Thus, we have work left to be done in last 3 days by the women's group. This also means th of work has been done by both the groups (before men left)
Now, (12 men + 12 women)'s 1 day work = =
i.e., work is done by 2 groups in 1 day.
So, of work is done by 2 groups together in = days
Total time take to complete the work will be
= + 3 =