A

Step 1: Understand the concept of specific heat. The specific heat of a material is defined as the amount of heat required to raise the temperature of a unit mass by one degree Celsius.

Step 2: Let the masses of the two bodies be m. Since they have the same heat capacities, we can say:
$C_1 = S_1 m$ and $C_2 = S_2 m$.

Step 3: The total heat capacity of the composite body, $C_t$, is the sum of the individual heat capacities:
$C_t = C_1 + C_2 = S_1 m + S_2 m = m(S_1 + S_2)$.

Step 4: The specific heat of the composite body, $S_c$, can be defined as:
$S_c = \frac{C_t}{m} = \frac{m(S_1 + S_2)}{m} = S_1 + S_2$.

Therefore, the specific heat of the composite body is the sum of the specific heats of the individual bodies. Hence, the final answer is:
$S_c = S_1 + S_2$.