Equating total work

Since the task is the same, set the work done by the first group equal to the second group: $8(4m + 6w) = 10(3m + 7w)$.

$32m + 48w = 30m + 70w$

Finding efficiency ratio

Simplify the equation to find the ratio between the efficiency of one man ($m$) and one woman ($w$): $2m = 22w$, so $m = 11w$.

$m = 11w$

Calculating total work in terms of women

Substitute $m = 11w$ into the first work equation: $\text{Total Work} = 8(4(11w) + 6w) = 8(44w + 6w) = 8(50w) = 400w$ units.

$\text{Total Work} = 400w$

Finding days for 10 women

To find the days ($d$) required for 10 women, use the relation $\text{Work} = \text{Efficiency} \times \text{Time}$. So, $400w = 10w \times d$.

$d = \frac{400w}{10w} = 40$