Mathematics for FinancePYQ 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

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.

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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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