The average weight of 12 persons increases by 2.5 kg when a new person comes in place of one of them weighing 48 kg. The weight of the new person is:

78

Let the average of 12 people be x kg

And the weight of the new person be y kg

Sum of 12 people weight is

 12 × x = 12x kg

When the person is replaced.

 12x + y - 48 = 12 × (x + 2.5 )

 12x + y - 48 = 12x + 30

 y = 48 + 30 = 78 kg

∴ The weight of the new person is 78 kg.