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

- 16
- 13
- 10
- 7

### Answer

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

As p = (c)(x),

x_{1}c_{1}/p_{1} = x_{2}c_{2}/p_{2}

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

xc/p = x_{2}(1.27c)/1.4p

x_{2} = 1.4x/1.27

x_{2} = 1.102x

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

**The correct option is C.**