Mathematics for FinancePYQ May 19Question 1285 of 512
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The population of a town increases every year by 2%\displaystyle 2\% of the population beginning of that year. The number of years by which the total increase of population be 40%\displaystyle 40\% is

Options

A7\displaystyle 7 years
B10\displaystyle 10 years
C17\displaystyle 17 years (apx.)
DNone of these
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Correct Answer

✅ Option c — 17\displaystyle 17 years (apx.)

All Options:

  • A7\displaystyle 7 years
  • B10\displaystyle 10 years
  • C17\displaystyle 17 years (apx.)
  • DNone of these

Detailed Solution & Explanation

**Derivation of Growth Period to Reach 40% Increase** Given: - Growth rate (r\displaystyle r) = 2%\displaystyle 2\% per annum - Target population increase = 40%\displaystyle 40\%, meaning Pt=1.40P0\displaystyle P_t = 1.40 P_0 **Step 1: Set up the growth equation** Pt=P0(1+r)tP_t = P_0(1 + r)^t 1.40P0=P0(1.02)t1.40 P_0 = P_0(1.02)^t 1.40=(1.02)t1.40 = (1.02)^t **Step 2: Solve for t\displaystyle t using logarithms** t=ln⁡(1.40)ln⁡(1.02)≈0.3364720.019803≈17 yearst = \frac{\ln(1.40)}{\ln(1.02)} \approx \frac{0.336472}{0.019803} \approx 17 \text{ years} Hence, **Option C** is the correct answer.

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