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 150\displaystyle 150 at 5%\displaystyle 5\% p.a. S.I. and to 100\displaystyle 100 at 3%\displaystyle 3\% p.a. S.I. Then the value of X\displaystyle X is

Options

A70\displaystyle 70
B40\displaystyle 40
C25\displaystyle 25
DNone of these
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Correct Answer

Option c25\displaystyle 25

All Options:

  • A70\displaystyle 70
  • B40\displaystyle 40
  • C25\displaystyle 25
  • DNone of these

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Detailed Solution & Explanation

**Derivation of Principal Investment Value** Given: - Amount at 5%\displaystyle 5\% p.a. simple interest = Rs. 150\displaystyle \text{Rs. }150 - Amount at 3%\displaystyle 3\% p.a. simple interest = Rs. 100\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 \text{--- (Equation 1)} 100=X(1+0.03t)— (Equation 2)100 = X(1 + 0.03 t) \quad \text{--- (Equation 2)} **Step 2: Divide Equation 1 by Equation 2** 150100=1+0.05t1+0.03t\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 = \frac{0.5}{0.005} = 100 \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 \times 100) 100=X(1+3)100 = X(1 + 3) 100=4X    X=1004=Rs. 25100 = 4 X \implies X = \frac{100}{4} = \text{Rs. }25 *(Note: The database lists Option A (70\displaystyle 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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