2women nd 5 men can together finish an embroider work in 4days while 3women nd 6 men can finish it in 3 days find the time to be taken by 1women alone 1men alone to finish the work
Answers
Heya dear...!!
Here is ur answer..!!
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→ Let the number of days taken by a woman be x
and
→ the number of days taken by a man be y.
⇒ 1 woman’s 1 day work =(1/x)th part of the work
⇒ And, 1 man’s 1 day work =(1/y)th part of the work
⇒ So, 2 women’s 1 day work =(2/x)th part of the work
⇒ And, 5 men’s 1 day work =(5/y)th part of the work
∴ 2 women and 5 men’s 1 day work =((2/x)+(5/y))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
↔ we can see that (1) = (2)
⇒2x+5y=14....................... (3)
Similarly, 3 women’s 1 day work =(3/x)th part of the work
And, 6 men’s 1 day work =(6/y)th part of the work
∴ 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)
↔ 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 an y=36
∴ 1 woman completes work in =18 days
And, 1 man completes work in =36 days
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