Mathematics for FinancePYQ Dec 23Question 1256 of 512
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The population of a city increases at the rate of 5%\displaystyle 5\% every year. What will be the population of the city in the year 2023\displaystyle 2023, if its population in 2021\displaystyle 2021 was 1,00,000\displaystyle 1,00,000?

Options

A1,05,000\displaystyle 1,05,000
B1,10,250\displaystyle 1,10,250
C1,15,240\displaystyle 1,15,240
D1,20,550\displaystyle 1,20,550
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Correct Answer

✅ Option b — 1,10,250\displaystyle 1,10,250

All Options:

  • A1,05,000\displaystyle 1,05,000
  • B1,10,250\displaystyle 1,10,250
  • C1,15,240\displaystyle 1,15,240
  • D1,20,550\displaystyle 1,20,550

Detailed Solution & Explanation

**Derivation of Population Growth** Given: - Population in 2021\displaystyle 2021 (P0\displaystyle P_0) = 1,00,000\displaystyle 1,00,000 - Growth rate (r\displaystyle r) = 5%\displaystyle 5\% per annum - Time (t\displaystyle t) = 2\displaystyle 2 years (from 2021\displaystyle 2021 to 2023\displaystyle 2023) **Step 1: Calculate the future population (P2\displaystyle P_2)** P2=P0(1+r)tP_2 = P_0(1 + r)^t P2=100000(1+0.05)2P_2 = 100000(1 + 0.05)^2 P2=100000(1.05)2P_2 = 100000(1.05)^2 P2=100000×1.1025=1,10,250P_2 = 100000 \times 1.1025 = 1,10,250 Hence, **Option B** is the correct answer.

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