Mathematics of FinanceMCQPYQ June 19Question 1195 of 512
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In SI if the principal is Rs. 2,000\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

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
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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

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Detailed Solution & Explanation

**Derivation of Simple Interest from Roots of Quadratic Equation** Given: - Principal (P\displaystyle P) = Rs. 2,000\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 \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 \times t = 5 \times 6 = 30 **Step 2: Calculate Simple Interest (SI\displaystyle SI)** SI=P×r×t100SI = \frac{P \times r \times t}{100} SI=2000×30100=Rs. 600SI = \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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More Questions from Mathematics of Finance

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

The simple interest on 600\displaystyle 600 for 9 months is 27\displaystyle 27. Find the interest rate.

Miss Liza lent 4,000\displaystyle 4,000 in such a way that some amount was given to Mr. A at 3%\displaystyle 3\% p.a. S.I. and rest amount to was given to B at 5%\displaystyle 5\% p.a. S.I., the annual interest from both is 144\displaystyle 144. Find the amount lent to Mr. A.

A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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