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Village Food Grain Production and Population Growth

CAT 2017 Slot 2 · Quantitative Ability · Medium · Percentages

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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. A.

    16

  2. B.

    13

  3. C.

    10

  4. D.

    7

Answer

C

Explanation

Per capita production = Total ProductionPopulation\frac{\text{Total Production}}{\text{Population}}.

Let initial production = PP, population = NN. New production = 1.40P1.40P. New per capita production = 1.27×PN1.27 \times \frac{P}{N}.

Let new population = N′N'. 1.40PN′=1.27×PN  ⟹  N′N=1.401.27≈1.10236\frac{1.40P}{N'} = 1.27 \times \frac{P}{N} \implies \frac{N'}{N} = \frac{1.40}{1.27} \approx 1.10236

Percentage increase in population ≈10.23%≈10%\approx 10.23\% \approx 10\%.

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