2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish in 3 days. find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone

 I think something is wrong, I did the calculations using substitution by Gaussian elimination and just bu normal substitution and solved them as linear equations in an augmented matrix and I always got the someone (in the matrix it was the woman) took a negative amount of hours to do it... Maybe it's your question? Maybe it's me, I'll give it another go.

I've thought of a way to show something isn't right. Imagine the first quadrant of a Cartesian graph. Say the y axis is the number of women, the x axis is the number of men. Now, the cooridantes 5,2 is the point were another lines (the days) is equal to 4 and 6,3 is where it is equal to 3. The gradient is obviously 1 and so it's reasonable to assume that 3,1 is equal to 2 that is, 1 woman and 3 men takes 2 days. Now, if 1 woman and 3 men take 3 days and 3 women and 6 men take 3 days... Either the men or the women are stopping work being done. So, it doesn't really work, and you can show it's the women by going on step further to 2,0 that is 2 men and no women the point on the new 'days' line would equal 1, and that implies it takes 2 days for 1 man to do the job, but it'd take a infinite amount of time for anything to get done by the women because it'd be a negative number, and again you can justify this by saying 2 men take 1 day, so 6 men should take a third of the day, and 6 men and 3 women take 3 days, which means the women are slowing down the men by 900%.... Forgive me if this is a bit rusty, I'm really tired.

 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

vry nice xplanation......

 thank u,pls ans my next ques written in ques sec,