Mathematics for FinancePYQ June 19Question 1191 of 512
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A sum was invested for 3\displaystyle 3 years as per C.I. and the rate of interest for first year is 9%\displaystyle 9\%, 2nd\displaystyle 2^{nd} year is 6%\displaystyle 6\% and 3rd\displaystyle 3^{rd} year is 3%\displaystyle 3\% p.a. respectively. Find the sum if the amount in three years is Rs. 550\displaystyle \text{Rs. }550?

Options

ARs. 250\displaystyle \text{Rs. }250
BRs. 300\displaystyle \text{Rs. }300
CRs. 462.16\displaystyle \text{Rs. }462.16
DRs. 350\displaystyle \text{Rs. }350
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Correct Answer

✅ Option c — Rs. 462.16\displaystyle \text{Rs. }462.16

All Options:

  • ARs. 250\displaystyle \text{Rs. }250
  • BRs. 300\displaystyle \text{Rs. }300
  • CRs. 462.16\displaystyle \text{Rs. }462.16
  • DRs. 350\displaystyle \text{Rs. }350

Detailed Solution & Explanation

**Derivation of Sum (Principal) for Successive Compound Interest Rates** Given: - Future Value (A\displaystyle A) = Rs. 550\displaystyle \text{Rs. }550 - Time (t\displaystyle t) = 3\displaystyle 3 years - Successive Rates: r1=9%\displaystyle r_1 = 9\% (1st year), r2=6%\displaystyle r_2 = 6\% (2nd year), r3=3%\displaystyle r_3 = 3\% (3rd year) **Step 1: Set up the successive compound interest equation** A=P(1+r1)(1+r2)(1+r3)A = P(1 + r_1)(1 + r_2)(1 + r_3) 550=P(1+9100)(1+6100)(1+3100)550 = P\left(1 + \frac{9}{100}\right)\left(1 + \frac{6}{100}\right)\left(1 + \frac{3}{100}\right) **Step 2: Substitute and simplify the expression** 550=P×1.09×1.06×1.03550 = P \times 1.09 \times 1.06 \times 1.03 550=P×1.190062550 = P \times 1.190062 **Step 3: Solve for P\displaystyle P** P=5501.190062≈Rs. 462.16P = \frac{550}{1.190062} \approx \text{Rs. }462.16 Hence, **Option C** is the correct answer.

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