$16 \cdot 15$ On line segment $A B$ there are two points $P$ and $Q$ on the same side of the midpoint of $A B, P$ divides $A B$ in the ratio $2: 3, Q$ divides $A B$ in the ratio $3: 4$, if $P Q=2$, then the length of $A B$ is
(A) 60.
(B) 70.
(C) 75.
(D) 80.
(E) 85.
(12th American High School Mathematics Examination, 1961)
[Solution] As shown in the figure, according to the given conditions,
$$
A P=\frac{2}{2+3} A B=\frac{2}{5} A B, \quad A Q=\frac{3}{4+3} A B=\frac{3}{7} A B,
$$

and $P Q=\frac{3}{7} A B-\frac{2}{5} A B=\frac{1}{35} A B=2$, which gives $A B=70$. Therefore, the correct choice is $(B)$.