CAT 2017 Slot 2 — QA Question 10

Total Food Production = Total Population × Per Capita Food Production 

Let the initial population be ‘p’ and the initial per capita food production be ‘c’

If f is the total food production, f = pc

This can also be rewritten as p = $\frac{f}{c}$

Now, as per given information, f increases to 1.4f and c increases to 1.27c.

So, if p₁ is population after increase.

1.4f = p₁(1.27c) 

$\frac{1.4f}{1.27c}$ = p₁ 

⇒ p₁ = $\left(\frac{1.4}{1.27}\right)\left(\frac{f}{c}\right)$

or p₁ = $\left(\frac{1.4}{1.27}\right)$(p) [$\left(âˆ\mu \mathrm{ p}=\frac{f}{c}\right)$ ]

$\Rightarrow$ p₁ â‰ƒ 1.1p 

This means that the population of the village has increased by approximately 10%.

Hence, option (c).