A survey of 120 households revealed that 70 do homestay business, 50 do agriculture business, and 30 do other work. Find N((H U A)') and draw a Venn diagram.

This set is the complement of the union of H and A, denoted as $(H \cup A)'$.

The cardinality notation for the number of households in this set is $N((H \cup A)')$.
From the given information, $N((H \cup A)') = 30$.

The cardinality notation is $\boxed{N((H \cup A)') = 30}$.

The Venn diagram would consist of a universal set $U$ (rectangle) containing two overlapping circles, $H$ and $A$.

• The region representing households doing only homestay business ($H$ only) has a value of 40.
• The region representing households doing only agriculture business ($A$ only) has a value of 20.
• The region representing households doing both homestay and agriculture business ($H \cap A$) has a value of 30.
• The region representing households doing neither homestay nor agriculture business ($(H \cup A)'$) is outside the circles but inside the universal set, and has a value of 30.

These are the households doing only homestay business or only agriculture business.

The number of households doing only one business is $\boxed{60}$.

Initially, $N((H \cup A)') = 30$. If 10 of these start homestay business, then:

The 10 households that previously did other work now do homestay business.
Initially, $N(H) = 70$.

The number of households doing agriculture business remains unchanged.

The ratio is $N(H)_{\text{new}} : N(A)_{\text{new}}$.

Simplify the ratio by dividing both sides by 10.

The ratio of homestay and agriculture business households is $\boxed{8:5}$.