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
Or
In another way
If you don't get the above way you can use this
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