4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?

Let men’s 1 day work =????

Let women’s 1 day work =????

4????+3????= $frac{1}{6}$ ………………(i)

5????+7????= $frac{1}{4}$ ……………..(ii)

∴ By solving eqn. (i) and (ii) —

????= $frac{1}{{78}}x = frac{5}{{156}}$

∴Required days = $frac{1}{{frac{1}{{78}} + frac{5}{{156}}}} = frac{1}{{frac{{2 + 5}}{{156}}}} = frac{{156}}{7} = 22frac{2}{7}$