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:
A. $$\frac{{65}}{4}$$
B. $$\frac{{93}}{3}$$
C. $$\frac{{51}}{5}$$
D. 60
Answer: Option C
Solution(By Examveda Team)
Let x be the required number of days 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 = $$\frac{1}{{14}}$$ And, 12 women's 1 day work = $$\frac{1}{{21}}$$ Then ,12 women's 3 days work = $$\frac{3}{{21}}$$ = $$\frac{1}{7}$$ The remaining work = $$1 - \frac{1}{7}$$ = $$\frac{6}{7}$$ Man's group leaves 3 days before the completion of work That is, they were working together for x - 3 days Thus, we have $$\frac{1}{7}$$ work left to be done in last 3 days by the women's group. This also means $$\frac{6}{7}$$ th of work has been done by both the groups (before men left) Now, (12 men + 12 women)'s 1 day work = $$\frac{1}{{14}} + \frac{1}{{21}}$$ = $$\frac{5}{{42}}$$ i.e., $$\frac{5}{{42}}$$ work is done by 2 groups in 1 day. So, $$\frac{6}{7}$$ of work is done by 2 groups together in $$\frac{{42}}{5} \times \frac{6}{7}$$ = $$\frac{{36}}{5}$$ days Total time take to complete the work will be= $$\frac{{36}}{5}$$ + 3 = $$\frac{{51}}{5}$$
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Comments ( 3 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
Suppose total time take to complete the work = x
(12*x-3)/12*14 + (12*x)/ 12*21 = 1
(x-3)/14 + x/ 21 =1
(3x -9+2x )/42 =1
5x = 51
X = 51/ 5
12 men work 1 day = 1/14
12 women work 1 day = 1/21
Let, the work complete in X days
Men are left 3 days before, that means ( x-3)
According to the question,
X-3/14 +x/21=1
Then, x= 51/5
The work complete 51/5 days
Ur ans is incomplete I think