1. Let the masses be: $m_1 = 8\,\text{kg}, \qquad m_2 = 2\,\text{kg}$

2. Since their kinetic energies are equal, $K_1 = K_2$

3. Using the kinetic energy formula in terms of momentum: $K = \frac{p^2}{2m}$

   So for the two bodies, $\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}$

4. Substitute the masses: $\frac{p_1^2}{2\cdot 8} = \frac{p_2^2}{2\cdot 2}$

   $\frac{p_1^2}{8} = \frac{p_2^2}{2}$

5. Cross-multiply: $p_1^2 = 4p_2^2$

   $p_1 = 2p_2$

6. Therefore, the ratio of their momenta is: $p_1 : p_2 = 2 : 1$

7. Matching with options:

   • A: $1:1$ ❌
   • B: $2:1$ ✅
   • C: $1:4$ ❌
   • D: $4:1$ ❌

Hence, the correct answer is B.