Explanation:

- Let the original numbers be $3x$ and $5x$.

- The new numbers after subtracting 4 are $(3x-4)$ and $(5x-4)$.

- According to the problem, $\frac{3x-4}{5x-4}=\frac{4}{7}$.

- Solve for $x$:

- Cross-multiply: $7(3x-4)=4(5x-4)$.

- Expand: $21x-28=20x-16$.

- Simplify: $21x-20x=28-16$.

- Result: $x=12$.

- The smaller original number is $3x=3\times 12=36$.

Option:4 - 36 is the correct answer.