Question

Q.2 women and 5 men together finish a work in 4 days.3 women and 6 men can finish it in 3 days .find the time taken by 1 women and men to finish the work.
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Answer 1

Let w and m represent women and men respectively

2W + 5M can do 1 work in 4 days

2W + 5M can do 1/4 work in 1 days

Also,

3W + 6M can do 1 work in 3days

3W + 6M can do 1/3 work in 1day

Then, equating work with men and women

2W + 5M =1/4.(i)

Then,

3W + 6M=1/3-(ii)

Or, 3(W + 2M)=1/3

Or,W + 2M =1/9-(iii)

Then subtracting (i) from (ii)

3W + 6M=1/3

-2W - 5M =-1/4)

W + M=1/3 -1/4

W + M= 1/12...............(iv)

Also,

Subtracting (iv) from (iii)

W + 2M =1/9

-W - M=-1/12

M = 1/9 – 1/12

Or, M=1/36

So subsituting m=1/36 in equation (iv)

W + 1/36 = 1/12

Or,W = 1/12 – 1/36

Hence, W=1/18

I men alone can do (1/36) work in 1 day

1 men alone can do 1 work in 36 days

Also,

1 women alone can do (1/18) in 1 day

1 women alone can do 1 work in 18 days



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