1. Let the masses be $m_1 = 4\,\text{g}, \qquad m_2 = 25\,\text{g}$

2. Since both bodies have equal kinetic energies, use the relation $K = \frac{p^2}{2m}$ where $p$ is linear momentum.

3. If kinetic energies are equal, then $\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}$

4. Rearranging, $\frac{p_1^2}{p_2^2} = \frac{m_1}{m_2}$

5. Taking square root, $\frac{p_1}{p_2} = \sqrt{\frac{m_1}{m_2}} = \sqrt{\frac{4}{25}} = \frac{2}{5}$

6. Therefore, the ratio of magnitudes of their linear momenta is $2:5$

7. Checking options:

   • A: $3:5$ ❌
   • B: $5:4$ ❌
   • C: $2:5$ ✅
   • D: $4:5$ ❌

Hence, the correct option is C.