Mathematics of FinanceMCQPYQ Nov 19Question 1196 of 512
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A man invests Rs. 12,000\displaystyle \text{Rs. }12,000 at 10%\displaystyle 10\% p.a. and another sum of money at 20%\displaystyle 20\% p.a. for one year. The total investment earns at 14%\displaystyle 14\% p.a. simple interest the total investment is:

Options

ARs. 8,000\displaystyle \text{Rs. }8,000
BRs. 20,000\displaystyle \text{Rs. }20,000
CRs. 14,000\displaystyle \text{Rs. }14,000
DRs. 16,000\displaystyle \text{Rs. }16,000
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Correct Answer

Option bRs. 20,000\displaystyle \text{Rs. }20,000

All Options:

  • ARs. 8,000\displaystyle \text{Rs. }8,000
  • BRs. 20,000\displaystyle \text{Rs. }20,000
  • CRs. 14,000\displaystyle \text{Rs. }14,000
  • DRs. 16,000\displaystyle \text{Rs. }16,000

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Detailed Solution & Explanation

**Derivation of Total Investment from Combined Simple Interest Rate** Given: - Investment 1 (P1\displaystyle P_1) = Rs. 12,000\displaystyle \text{Rs. }12,000 at rate r1=10%\displaystyle r_1 = 10\% p.a. - Investment 2 (P2\displaystyle P_2) = S\displaystyle S (unknown sum) at rate r2=20%\displaystyle r_2 = 20\% p.a. - Time (t\displaystyle t) = 1\displaystyle 1 year - Overall average interest rate earned = 14%\displaystyle 14\% p.a. **Step 1: Express total interest earned** Interest from P1=12000×10×1100=Rs. 1,200\text{Interest from } P_1 = \frac{12000 \times 10 \times 1}{100} = \text{Rs. }1,200 Interest from P2=S×20×1100=0.20S\text{Interest from } P_2 = \frac{S \times 20 \times 1}{100} = 0.20 S Total Interest Earned=1200+0.20S\text{Total Interest Earned} = 1200 + 0.20 S **Step 2: Express interest using the average rate on total investment (P1+P2\displaystyle P_1 + P_2)** Total Interest=(12000+S)×14×1100=0.14(12000+S)=1680+0.14S\text{Total Interest} = \frac{(12000 + S) \times 14 \times 1}{100} = 0.14(12000 + S) = 1680 + 0.14 S **Step 3: Equate the two expressions and solve for S\displaystyle S** 1200+0.20S=1680+0.14S1200 + 0.20 S = 1680 + 0.14 S 0.20S0.14S=168012000.20 S - 0.14 S = 1680 - 1200 0.06S=4800.06 S = 480 S=4800.06=Rs. 8,000S = \frac{480}{0.06} = \text{Rs. }8,000 **Step 4: Find the total investment** Total Investment=P1+P2=12000+8000=Rs. 20,000\text{Total Investment} = P_1 + P_2 = 12000 + 8000 = \text{Rs. }20,000 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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