Question

In a village, the production of food grain
is increased
by 40%. 4 per capita
Production
of food grains increased
by
27% during
a certain period.
The percentage by
which the population
village increased during the
same period is -​

Answer 1

Answer:

Population  increased ≈ 10%

Step-by-step explanation:

Let the population=100y

and the Initial production of food grains =100x

Thus Initial per capita production = 100x/100y=x/y

Now

Food grain production is increased by 40%=40x

New production=140x

If population is increased by p% then

new population =100y+p*100y/100

=100y+py=y(100+p)

New per capita food production

=140x/(100y+py) =140x / y(100+p)

% increase in per capita food

=100*( 140x / y(100+p) - x/y) / ( x/y)=27 ( Given)

100x/y { 140 /(100+p) -1} / (x/y) = 27

100 { 140/(100+p)-1}=27

14000/(100+p) -100=27

14000/(100+p) =127

14000=12700+127p

127p=14000-12700

127p=1300

p=1300/127

=10.26% ≈ 10%