Mathematics of FinanceMCQPYQ Jan 21Question 1212 of 512
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A certain sum amounted to 575\displaystyle 575 at 5%\displaystyle 5\% in a time in which 750\displaystyle 750 amounted to 840\displaystyle 840 at 4%\displaystyle 4\%. If the rate of interest is simple, find the sum -

Options

A525\displaystyle 525
B550\displaystyle 550
C515\displaystyle 515
D500\displaystyle 500
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Correct Answer

✅ Option d — 500\displaystyle 500

All Options:

  • A525\displaystyle 525
  • B550\displaystyle 550
  • C515\displaystyle 515
  • D500\displaystyle 500

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Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - For Case 1: Principal = P\displaystyle P, Rate = 5%\displaystyle 5\% S.I., Amount = Rs. 575\displaystyle \text{Rs. }575 in time t\displaystyle t. - For Case 2: Principal = Rs. 750\displaystyle \text{Rs. }750, Rate = 4%\displaystyle 4\% S.I., Amount = Rs. 840\displaystyle \text{Rs. }840 in time t\displaystyle t. **Step 1: Calculate time (t\displaystyle t) from Case 2** Simple Interest earned in Case 2=A2−P2=840−750=Rs. 90\text{Simple Interest earned in Case 2} = A_2 - P_2 = 840 - 750 = \text{Rs. }90 Using the Simple Interest formula: SI2=P2×r2×t100SI_2 = \frac{P_2 \times r_2 \times t}{100} 90=750×4×t10090 = \frac{750 \times 4 \times t}{100} 90=30t  ⟹  t=3 years90 = 30 t \implies t = 3 \text{ years} **Step 2: Solve for Case 1 principal (P\displaystyle P) with t=3\displaystyle t = 3 years** A1=P(1+r1×t100)A_1 = P\left(1 + \frac{r_1 \times t}{100}\right) 575=P(1+5×3100)575 = P\left(1 + \frac{5 \times 3}{100}\right) 575=P(1+0.15)575 = P(1 + 0.15) 575=1.15P575 = 1.15 P P=5751.15=Rs. 500P = \frac{575}{1.15} = \text{Rs. }500 Hence, **Option D** 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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