$32 \cdot 35$ A two-digit number, when the tens digit and the units digit are swapped, the resulting two-digit number is $\frac{7}{4}$ times the original number. How many such two-digit numbers are there?
(A) 1.
(B) 2.
(C) 4.
(D) Infinitely many.
(E) 0.
(China Junior High School Mathematics League, 1984)
[Solution] Let the tens digit of the original number be $a$, and the units digit be $b$. According to the problem, we have $-\frac{7}{4}(10 a+$
$b)=10 b+a$, which simplifies to $2 a \doteq b$.
$\because \quad 1 \leqslant a, \quad b \leqslant 9$,
$\therefore a=1,2,3,4$, then $b=2,4,6,8$.
The numbers that meet the conditions are: $12,24,36,48$, a total of four.
Therefore, the answer is $(C)$.