Mathematics of FinanceMCQMTP Jun 23 Series IIQuestion 1381 of 512
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Mr. A invested X\displaystyle X in an organization, it amounts to $150at\displaystyle at5\%$ p.a. S.I. and to $100$ at 3%\displaystyle 3\% p.a. S.I. Then the value of X\displaystyle X is

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

✅ Option c — $25$

All Options:

  • A$70$
  • B$40$
  • C$25$
  • DNone of these

Detailed Solution & Explanation

**Derivation of Principal Investment Value** Given: - Amount at 5%\displaystyle 5\% p.a. simple interest = Rs. 150\displaystyle Rs. \displaystyle \text{Rs. }150 - Amount at 3%\displaystyle 3\% p.a. simple interest = Rs. 100\displaystyle Rs. \displaystyle \text{Rs. }100 - Let X\displaystyle X be the principal sum and t\displaystyle t be the time period in years. **Step 1: Formulate the equations for both cases** 150=X(1+0.05t)— (Equation 1)150 = X(1 + 0.05 t) \quad — (Equation 1)\displaystyle \text{--- (Equation 1)} 100=X(1+0.03t)— (Equation 2)100 = X(1 + 0.03 t) \quad — (Equation 2)\displaystyle \text{--- (Equation 2)} **Step 2: Divide Equation 1 by Equation 2** 150100=1+0.05t1+0.03t\displaystyle \frac{150}{100} = \frac{1 + 0.05 t}{1 + 0.03 t} 1.5(1+0.03t)=1+0.05t1.5(1 + 0.03 t) = 1 + 0.05 t 1.5+0.045t=1+0.05t1.5 + 0.045 t = 1 + 0.05 t 0.5=0.005t  ⟹  t=0.50.005=100 years0.5 = 0.005 t \implies t = 0.50.005=100\displaystyle \frac{0.5}{0.005} = 100  years\displaystyle \text{ years} **Step 3: Solve for X\displaystyle X** Substitute t=100\displaystyle t = 100 into Equation 2: 100=X(1+0.03×100)100 = X(1 + 0.03 ×\displaystyle \times 100) 100=X(1+3)100 = X(1 + 3) 100=4X  ⟹  X=1004=Rs. 25100 = 4 X \implies X = \displaystyle \frac{100}{4} = \text{Rs. }25 *(Note: The database lists Option A ($70$) as correct, which is a typo in the key. The mathematically correct principal is 25, which is Option C.)* Hence, **Option C** 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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