2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days.find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
Answers
Let time taken by 1 woman alone to finish the work =x days
Let time taken by 1 man alone to finish the work =y days
So, 1 woman’s 1 day work =(1x)th part of the work
And, 1 man’s 1 day work =(1y)th part of the work
So, 2 women’s 1 day work =(2x)th part of the work
And, 5 men’s 1 day work =(5y)th part of the work
Therefore, 2 women and 5 men’s 1 day work =((2x)+(5y))th part of the work (1)
It is given that 2 women and 5 men complete work in = 4 days
It means that in 1 day, they will be completing 14th part of the work. (2)
Clearly, we can see that (1) = (2)
⇒2x+5y=14 (3)
Similarly, 3 women’s 1 day work =(3x)th part of the work
And, 6 men’s 1 day work =(6y)th part of the work
Therefore, 3 women and 6 men’s 1 day work =((3x)+(6y))th part of the work (4)
It is given that 3 women and 6 men complete work in = 3 days
It means that in 1 day, they will be completing 13rd part of the work. (5)
Clearly, we can see that (4) = (5)
⇒3x+6y=13 (6)
Let 1x=p and 1y=q
Putting this in (3) and (6), we get
2p+5q=14 and 3p+6q=13
⇒8p+20q=1 (7) and 9p+18q=1 (8)
Multiplying (7) by 9 and (8) by 8, we get
72p+180q=9 (9)
72p+144q=8 (10)
Substracting (10) from (9), we get
36q=1
⇒q=136
Putting this in (8), we get
9p+18(136)=1
⇒9p+12=1
⇒9p=1−12=12
⇒p=118
Putting values of p and q in (1x=p and 1y=q), we get
x=18 and y=36
Therefore, 1 woman completes work in =18 days
And, 1 man completes work in =36 days
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Answer:
Number of days taken by a woman = 18 days
Number of days taken by a man = 36 days
Step-by-step explanation:
