In a company, initially the ratio of the foreign and domestic workers was 5 : 8. When some foreign and 12 domestic workers left the company, this ratio became 2 : 3. Later, when 10 more foreign workers were replaced by 10 new domestic workers, this ratio became 3 : 7. The initial number of domestic workers in the company was ___________

Initial ratio Foreign:Domestic = 5:8. Let F = 5k, D = 8k.

Stage 1: Some foreign + 12 domestic leave; ratio becomes 2:3. So $$\dfrac{F-x}{D-12} = \dfrac{2}{3}$$, i.e., $$3(5k-x) = 2(8k-12) \Rightarrow 15k - 3x = 16k - 24 \Rightarrow x = \dfrac{24-k}{3}$$.

Stage 2: 10 foreign replaced by 10 new domestic, ratio becomes 3:7. New foreign = $$(5k-x) - 10$$; new domestic = $$(8k-12)+10 = 8k-2$$. So $$\dfrac{5k-x-10}{8k-2} = \dfrac{3}{7}$$.

Solving with $$x = (24-k)/3$$ gives $$k = 9$$. Initial domestic = $$8 \times 9 = 72$$.