Question

Total income of a country increases by 40% in a year while its population increases by 30%. What is the change in its per capita income over the last year?

Answer 1

suppose this year country's income is Rs . x
and that popualtion is y

now its per capita income =  income/ population = x/y

A`/Q  income increases by 40 %  implies = x . 40/100
                                                                 =  4x/10
                     so new national income = x + 4x/10 = 14x/10

similarly  poulation increase by  30% = y . 30/100 = 3y/10
             so population this yr = y + 3y/10 = 13y/10

therefore income per capita this yr = 14x/10/13y/10 = 14x/13y

now change in per capita income = 14x/13y - x/y = x/13y

                         percentage increase = x/13y /  x/y    x 100
                                                       = 7.69%


hope my ans is correct............any doubts then ask.