Question

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

• A. 16
• B. 13
• C. 10
• D. 7

Answer 1

The Correct Option is C

To find the percentage increase in the population, we can use the formula relating production, per capita production, and population:

The relationship is given by:

\[ \text{Total Production} = \text{Population} \times \text{Per Capita Production} \]

Given that:

• Total Production increased by 40%.
• Per Capita Production increased by 27%.

Let the original Total Production be \(P\), and the original Population be \(N\).

Let's denote:

• Increased Total Production = \(1.4P\)
• Increased Per Capita Production = \(1.27 \times \text{Original Per Capita Production}\)

Therefore, the equation becomes:

\[ 1.4P = N_{\text{new}} \times 1.27 \times \frac{P}{N} \]

Thus, we have:

\[ N_{\text{new}} = \frac{1.4P}{1.27 \times \frac{P}{N}} \]

\[ N_{\text{new}} = \frac{1.4N}{1.27} \]

The increase in population is:

\[ N_{\text{increase}} = N_{\text{new}} - N \]

\[ N_{\text{increase}} = \frac{1.4N}{1.27} - N \]

\[ N_{\text{increase}} = \left(\frac{1.4}{1.27} - 1\right)N \]

The percentage increase in population is:

\[ \%\text{Increase} = \left(\frac{1.4}{1.27} - 1\right) \times 100\% \]

\[ \%\text{Increase} = \left(\frac{1.4 - 1.27}{1.27}\right) \times 100\% \]

\[ \%\text{Increase} \approx 0.1024 \times 100\% = 10.24\% \]

Thus, the nearest whole number to the percentage increase is 10%.

The correct answer is: 10