Q84 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

The population of a city grows at the annual rate of \(3 \%\). What percentage increase is expected in \(5 \mathrm{yr}\) ?

  • A
    \(12.9 \%\)
  • B
    \(13.9 \%\)
  • C
    \(14.9 \%\)
  • Correct answer
    D
    \(15.9 \%\)

Solution

Let the population in begining is \(P_0\), then according to the question percentage increase in 5 yr expected is \(\begin{aligned} \frac{P_0\left(1+\frac{3}{100}\right)^5-P_0}{P_0} \times 100 & =\left[\left(\frac{103}{100}\right)^5-1\right] \times 100 \\ & =\left[(1.03)^5-1\right] \times 100 \\ & =[1.159-1] \times 100=15.9 \% \end{aligned}\) Hence, option (d) is correct.

Hence, the correct answer is option: 'D'.

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