Here the number of articles to be made is same in each case so it can be consider as total work.

Part of the work 5 men can do in one day = 1/18

Part of the work 1 man can do in one day = $(\frac{1}{{18 \times 5}}{\rm{\;}} = {\rm{\;}}\frac{1}{{90}})$

Part of the work 20 women can do in one day = 1/6

Part of the work 1 woman can do in one day = $(\frac{1}{{6 \times 20}}{\rm{\;}} = {\rm{\;}}\frac{1}{{120}})$

Part of the work 15 children can do in one day = 1/10

Part of the work 1 child can do in one day = $(\frac{1}{{15 \times 10}}{\rm{\;}} = {\rm{\;}}\frac{1}{{150}})$

Part of the work 12 men, 10 women and 5 children can do in 3 days = $(3 \times \left( {\frac{{12}}{{90}} + \frac{{10}}{{120}} + \frac{5}{{150}}} \right))$

⇒ Part of work finished = $(\frac{{12}}{{30}} + \frac{{10}}{{40}} + \frac{5}{{50}}{\rm{\;}} = {\rm{\;}}\frac{2}{5} + \frac{1}{4} + \frac{1}{{10}}{\rm{\;}} = {\rm{\;}}\frac{{8 + 5 + 2}}{{20}}{\rm{\;}} = {\rm{\;}}\frac{{15}}{{20}}{\rm{\;}} = {\rm{\;}}\frac{3}{4})$

Remaining work = $(1 - \frac{3}{4}{\rm{\;}} = {\rm{\;}}\frac{1}{4})$

Let us assume we need n women to complete the remaining work in one day,

Then Part of the work n women can do in one day = $(\frac{{\rm{n}}}{{120}}{\rm{\;}} = {\rm{\;}}\frac{1}{4})$