Mathematics for FinancePYQ Dec 21Question 1227 of 512
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A sum of x\displaystyle x amounts to 27,900\displaystyle 27,900 in 3\displaystyle 3 years and to 41,850\displaystyle 41,850 in 6\displaystyle 6 years at a certain rate percent per annum, when the interest is compounded yearly. The value of x\displaystyle x is:

Options

A16,080\displaystyle 16,080
B18,600\displaystyle 18,600
C18,000\displaystyle 18,000
D16,800\displaystyle 16,800
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Correct Answer

✅ Option b — 18,600\displaystyle 18,600

All Options:

  • A16,080\displaystyle 16,080
  • B18,600\displaystyle 18,600
  • C18,000\displaystyle 18,000
  • D16,800\displaystyle 16,800

Detailed Solution & Explanation

**Derivation of Principal Amount in Compound Interest** Given: - Amount after 3\displaystyle 3 years (A3\displaystyle A_3) = Rs. 27,900\displaystyle \text{Rs. }27,900 - Amount after 6\displaystyle 6 years (A6\displaystyle A_6) = Rs. 41,850\displaystyle \text{Rs. }41,850 - Interest is compounded yearly. **Step 1: Set up the Amount equations** A3=x(1+r)3=27900A_3 = x(1 + r)^3 = 27900 A6=x(1+r)6=41850A_6 = x(1 + r)^6 = 41850 **Step 2: Divide the two equations to find (1+r)3\displaystyle (1+r)^3** A6A3=x(1+r)6x(1+r)3\frac{A_6}{A_3} = \frac{x(1+r)^6}{x(1+r)^3} 4185027900=(1+r)3\frac{41850}{27900} = (1+r)^3 (1+r)3=1.5(1+r)^3 = 1.5 **Step 3: Solve for Principal (x\displaystyle x)** Substitute (1+r)3=1.5\displaystyle (1+r)^3 = 1.5 back into the A3\displaystyle A_3 equation: x×1.5=27900x \times 1.5 = 27900 x=279001.5=Rs. 18,600x = \frac{27900}{1.5} = \text{Rs. }18,600 Hence, **Option B** is the correct answer.

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