in a village, the production of food grains increased by 40%, and their personal captia production of food grains during a certain period increased by 27%. the percentage by which the population of the village increased during the same period is

Previous year -
Previous food production : x kg
Number of people = y
Per capita consumption (kg) = x/y

Now -
Food production = [1 + (40/100)]* x = 1.4*x
Number of people = Y
Per capita consumption = 1.4*x/Y = 1.27*(x/y)

Comparing we get :
1.4/Y = 1.27/y
Y = (1.4/1.27) * y

% increase = (1.4/1.27 - 1)*100 = 10.23%