jmc

Let $x$ be number of people wearing all three items. Since 30 people are wearing bathing suits and sunglasses, we know that $30-x$ are wearing just bathing suits and sunglasses. Similarly, $25-x$ are wearing just bathing suits and hats, while $40-x$ are wearing just sunglasses and a hat.

To find the number of people wearing just sunglasses, we subtract the people who are wearing sunglasses with other items from the total number of people wearing sunglasses, which is $110-(30-x)-(40-x)-x=40+x$. Similarly, the number of people wearing just hats is $30+x$, while the number of people wearing just bathing suits is $15+x$.

Since the total number of people on the beach is 190, and everyone is wearing one of the items, we have: $$\begin{array}{rl}190& =(15+x)+(40+x)+(30+x)\\ & +(25-x)+(30-x)+(40-x)+x\\ & =180+x.\end{array}$$ We can then solve for $x$, so the number of people on the beach wearing all three items is $x=\boxed{10}$.