smc

Let $d$ be the number of doctors and $l$ be the number of lawyers. The average age of the doctors is $35$, so the sum of the doctors' ages is $35d$. The average age of the lawyers is $50$, so the sum of the lawyers' ages is $50l$. With the two information, we can write an equation. $$\frac{35d+50l}{d+l}=40$$ $$35d+50l=40d+40l$$ $$10l=5d$$ $$\frac{d}{l}=2$$ The ratio of the number of doctors to the number of lawyers is $\boxed{2:1}$.