2 men and 1 woman can do a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a men gets ? 90 per day, what should be the wages per day of a women?

Let man be represented by m and woman be represented by w.
? 2m + 1w = 1/14
? 14 x (2m + 1w ) = 1 ...(i)

and 4w + 2m = 1/8
8 x (4w + 2m) = 1 ...(ii)

On equating Eqs. (i) and (ii), we get
14 (2m + 1w) = 8 (4w + 2m)
? 28m + 14w = 32w + 16m
? 28m - 16m = 32w - 14w
? 12m = 18w
? m/w = 18/12 = 3/2
So, efficiency of 1 man and 1 woman is 3 : 2.
So, their wages must be in the same ratio
90/x = 3/2
[here, x = wages of a woman ]
? x = 90 x 2 / 3 = ? 60