Mathematics of FinanceMCQPYQ June 19Question 1195 of 512
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In SI if the principal is Rs. 2,000\displaystyle Rs. \displaystyle \text{Rs. }2,000 and the rate and time are the roots of the equation x2−11x+30=0\displaystyle x^2 - 11x + 30 = 0 then SI is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — Rs. 600\displaystyle \text{Rs. }600

All Options:

  • ARs. 500\displaystyle \text{Rs. }500
  • BRs. 600\displaystyle \text{Rs. }600
  • CRs. 700\displaystyle \text{Rs. }700
  • DRs. 800\displaystyle \text{Rs. }800

Detailed Solution & Explanation

**Derivation of Simple Interest from Roots of Quadratic Equation** Given: - Principal (P\displaystyle P) = Rs. 2,000\displaystyle Rs. \displaystyle \text{Rs. }2,000 - Rate (r\displaystyle r) and Time (t\displaystyle t) are roots of the quadratic equation: x2−11x+30=0x^2 - 11x + 30 = 0 **Step 1: Find the roots of the quadratic equation** x2−5x−6x+30=0x^2 - 5x - 6x + 30 = 0 x(x−5)−6(x−5)=0x(x - 5) - 6(x - 5) = 0 (x−5)(x−6)=0  ⟹  x=5 or x=6(x - 5)(x - 6) = 0 \implies x = 5  or \displaystyle \text{ or } x = 6 So the rate and time are 5\displaystyle 5 and 6\displaystyle 6 (either r=5%\displaystyle r=5\%, t=6\displaystyle t=6 years or r=6%\displaystyle r=6\%, t=5\displaystyle t=5 years). In both cases, the product of rate and time is: r×t=5×6=30r ×\displaystyle \times t = 5 ×\displaystyle \times 6 = 30 **Step 2: Calculate Simple Interest (SI\displaystyle SI)** SI=P×r×t100SI = P×r×t100\displaystyle \frac{P \times r \times t}{100} SI=2000×30100=Rs. 600SI = \displaystyle \frac{2000 \times 30}{100} = \text{Rs. }600 Hence, **Option B** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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