Set up the work equation

Let 1 man's 1-day work be $M$ and 1 woman's 1-day work be $W$. Since total work is constant in both scenarios, we can equate them:

$(8M + 12W) \times 10 = (6M + 8W) \times 14$

Find the efficiency ratio

Expanding and simplifying the equation to find the relationship between $M$ and $W$:

$80M + 120W = 84M + 112W \implies 4M = 8W \implies M = 2W$

Calculate Total Work

Substitute $M = 2W$ into the first equation to find total work in terms of woman-days:

$\text{Total Work} = (8(2W) + 12W) \times 10 = 28W \times 10 = 280 \text{ units}$

Calculate individual days

Time taken by 1 woman alone = $280 / 1 = 280$ days. Time taken by 1 man alone = $280 / 2 = 140$ days.

$280 - 140 = 140 \text{ days}$