Mathematics for FinancePYQ Nov 19Question 1372 of 512
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What will be the population after 3\displaystyle 3 years when present population is Rs. 25,000\displaystyle \text{Rs. }25,000 and population increases at the rate of 3%\displaystyle 3\% in 1st\displaystyle 1^{st} year, at 4%\displaystyle 4\% in 2nd\displaystyle 2^{nd} year and 5%\displaystyle 5\% in 3rd\displaystyle 3^{rd} year?

Options

ARs. 28,119\displaystyle \text{Rs. }28,119
BRs. 29,118\displaystyle \text{Rs. }29,118
CRs. 27,000\displaystyle \text{Rs. }27,000
DRs. 30,000\displaystyle \text{Rs. }30,000
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Correct Answer

✅ Option a — Rs. 28,119\displaystyle \text{Rs. }28,119

All Options:

  • ARs. 28,119\displaystyle \text{Rs. }28,119
  • BRs. 29,118\displaystyle \text{Rs. }29,118
  • CRs. 27,000\displaystyle \text{Rs. }27,000
  • DRs. 30,000\displaystyle \text{Rs. }30,000

Detailed Solution & Explanation

**Derivation of Population after 3 Years** Given: - Present Population (P0\displaystyle P_0) = 25,000\displaystyle 25,000 - Growth rate in year 1 (r1\displaystyle r_1) = 3%\displaystyle 3\% - Growth rate in year 2 (r2\displaystyle r_2) = 4%\displaystyle 4\% - Growth rate in year 3 (r3\displaystyle r_3) = 5%\displaystyle 5\% **Step 1: Set up the compound growth formula for successive rates** P3=P0(1+r1)(1+r2)(1+r3)P_3 = P_0(1 + r_1)(1 + r_2)(1 + r_3) P3=25000(1+3100)(1+4100)(1+5100)P_3 = 25000\left(1 + \frac{3}{100}\right)\left(1 + \frac{4}{100}\right)\left(1 + \frac{5}{100}\right) **Step 2: Calculate the population** P3=25000×1.03×1.04×1.05P_3 = 25000 \times 1.03 \times 1.04 \times 1.05 P3=25750×1.04×1.05P_3 = 25750 \times 1.04 \times 1.05 P3=26780×1.05=28,119P_3 = 26780 \times 1.05 = 28,119 Hence, **Option A** is the correct answer.

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