In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

1. 16
2. 13
3. 10
4. 7

Let the initial production be p, population be x and the initial per capita consumption be c.

As p = (c)(x),

x1c1/p1 = x2c2/p2

Finally, production became 1.4p and per capita consumption became 1.27c

xc/p = x2(1.27c)/1.4p

x2 = 1.4x/1.27

x2 = 1.102x

Therefore, population (x) increased by approximately 10%.

The correct option is C.