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CAT 2017 Slot 2 — QA Question 10

PercentageEasy

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

Answer & solution

Correct answer: 10

  • A

    16

  • B

    13

  • 10

  • D

    7

Solution

Easy

Use total == population ×\times per-capita. Population is the ratio of total production to per-capita production, so the population's growth factor is the ratio of the other two growth factors.

1

Relate the three quantities. With ff total food, pp population, cc per-capita: f=pcf=pc, so p=fcp=\dfrac{f}{c}.

p=fc\begin{aligned} &p=\frac{f}{c} \end{aligned}
2

Apply the growth factors. Total rises by 40%40\% (×1.40\times1.40) and per-capita by 27%27\% (×1.27\times1.27).

pnew=1.40 f1.27 c=1.401.27 p\begin{aligned} &p_{\text{new}}=\frac{1.40\,f}{1.27\,c}=\frac{1.40}{1.27}\,p \end{aligned}
3

Read off the percentage rise.

1.401.27≈1.102⇒ pnew≈1.10 p(about +10%)\begin{aligned} &\frac{1.40}{1.27}\approx 1.102\\ &\Rightarrow\ p_{\text{new}}\approx 1.10\,p \quad\text{(about }+10\%\text{)} \end{aligned}
Population increase≈10%\text{Population increase}\approx 10\%

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CAT 2017 Slot 2 QA Q10: In a village, the production of food grains increased by 40% and the per capita production of food grains incr — Solution | TheCATExam