Heat capacity means Q/∆t is same. However, specific heat means (Q/∆t) * 1/m

As we can see, there is a slight difference between specific heat and heat capacity. Specific heat is the amount of heat needed to raise the temperature of one kilogram of mass by 1 degree. The heat capacity is the amount of heat needed to raise the temperature of the substance by 1 degree.

It is given in the problem that the heat capacity is the same for two bodies. So (Q/∆t) is the same. But as specific heat capacity is C₁ and C₂, their masses would be different. Let us assume that to be m₁ and m₂ respectively.

C₁ = Q/m₁∆t and C₂ = Q/m₂∆t

Now, the specific capacity of the composite body is C_c = Q / ∆t  * 1/ (m₁ + m₂)

m₁ + m₂ = Q/∆t (1/C₁ + 1/C₂) = Q/∆t (C₁ + C₂ / C₁ C₂ )

Hence, C_c = Q / ∆t  * 1/ (m₁ + m₂)

                = C₁ C₂ / (C₁ + C₂)