Mathematics for FinancePYQ Jan 21Question 1214 of 512
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The population of a town increase by 2%\displaystyle 2\% of the population at the beginning of the year. The number of year by which the total increases in population would be 40%\displaystyle 40\% is:

Options

A7\displaystyle 7 years
B10\displaystyle 10 years
C17\displaystyle 17 years
D19\displaystyle 19 years (approx.)
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Correct Answer

✅ Option c — 17\displaystyle 17 years

All Options:

  • A7\displaystyle 7 years
  • B10\displaystyle 10 years
  • C17\displaystyle 17 years
  • D19\displaystyle 19 years (approx.)

Detailed Solution & Explanation

**Derivation of Time for Population to Increase by 40%** Given: - Present Population = P0\displaystyle P_0 - Annual growth rate (r\displaystyle r) = 2%\displaystyle 2\% per annum - Target Increase = 40%\displaystyle 40\%, meaning final population Pn=1.40P0\displaystyle P_n = 1.40 P_0. **Step 1: Set up the geometric growth equation** Pn=P0(1+r)nP_n = P_0(1 + r)^n 1.40P0=P0(1+0.02)n1.40 P_0 = P_0(1 + 0.02)^n 1.40=(1.02)n1.40 = (1.02)^n **Step 2: Solve for n\displaystyle n using logarithms** ln⁡(1.40)=nln⁡(1.02)\ln(1.40) = n \ln(1.02) n=ln⁡(1.40)ln⁡(1.02)n = \frac{\ln(1.40)}{\ln(1.02)} Using log values: ln⁡(1.40)≈0.336472\ln(1.40) \approx 0.336472 ln⁡(1.02)≈0.019803\ln(1.02) \approx 0.019803 n=0.3364720.019803≈16.99 years≈17 yearsn = \frac{0.336472}{0.019803} \approx 16.99 \text{ years} \approx 17 \text{ years} Hence, **Option C** is the correct answer.

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