Question

In a village, the production of food grains increased by 44%, and the per capita production of food grains increased by 25% during a certain period. The percentage by which the population of the village increased during the same period is nearest to:

(a) 15%
(b) 20%
(c) 25%
(d) 30%

Answer 1

The population of the village increased by approximately 15% when comparing the increase in food grain production and the per capita increase rate of food grains.

Step-by-step explanation:

To find the percentage by which the population of the village increased, let the initial production of food grains be P and the initial population be N. After the increase, the production became 1.44P (since it increased by 44%) and the per capita production increased from P/N to 1.25(P/N) because of the 25% increase. With the increase in population to, let's say, N', the new per capita production would be 1.44P/N'.

We set the equations equal to each other because the per capita production is the same in both equations:

1.25(P/N) = 1.44P/N'

From this ratio, we can find N' in terms of N:

N' = 1.44/1.25 × N

N' = 1.152 × N

Therefore, the population increased by ((N' - N)/N) × 100% which equals ((1.152N - N)/N) × 100% = 15.2%.

The answer that best approximates this result is (a) 15%.