Answer: 

Cat and mouse weigh 10 kg

dog and mouse weigh 20 kg

-> Dog is heavier than cat: 20 - 10 = 10 (kg)

But dog and cat weigh 24 kg

According to the sum of the differences

-> Dog weighs: (24 + 10) : 2 = 17 (kg)

Cat weighs: 24 - 17 = 7 (kg)

Mouse weighs: 10 - 7 = 3 (kg)

So dog, cat and mouse weigh:

17 + 7 + 3 = 27 (kg)