Mathematics of FinanceMCQMTP Dec 22 Series IIQuestion 1376 of 512
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8,829\displaystyle 8,829 is invested into three different sectors in such a way that their amounts at 4%\displaystyle 4\% p.a. S.I. after 5\displaystyle 5 years; 6\displaystyle 6 and 8\displaystyle 8 years are equal. Find each part of the sum.

Options

A3,069;2,970;2,790\displaystyle 3,069; 2,970; 2,790
B3,089;2,970;2,790\displaystyle 3,089; 2,970; 2,790
C3,690;2,970;2,790\displaystyle 3,690; 2,970; 2,790
D3,069;2,960;2,760\displaystyle 3,069; 2,960; 2,760
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Correct Answer

✅ Option a — 3,069;2,970;2,790\displaystyle 3,069; 2,970; 2,790

All Options:

  • A3,069;2,970;2,790\displaystyle 3,069; 2,970; 2,790
  • B3,089;2,970;2,790\displaystyle 3,089; 2,970; 2,790
  • C3,690;2,970;2,790\displaystyle 3,690; 2,970; 2,790
  • D3,069;2,960;2,760\displaystyle 3,069; 2,960; 2,760

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Detailed Solution & Explanation

**Derivation of Sector Investments** Given: - Total sum to invest = Rs. 8,829\displaystyle \text{Rs. }8,829 - Rate of Interest (R\displaystyle R) = 4%\displaystyle 4\% per annum simple interest - Time periods for the three parts: t1=5\displaystyle t_1 = 5 years, t2=6\displaystyle t_2 = 6 years, t3=8\displaystyle t_3 = 8 years - Amounts after these periods are equal. **Step 1: Set up the equal amounts relation** Let the three parts be x\displaystyle x, y\displaystyle y, and z\displaystyle z. A1=x(1+0.04×5)=1.20xA_1 = x(1 + 0.04 \times 5) = 1.20 x A2=y(1+0.04×6)=1.24yA_2 = y(1 + 0.04 \times 6) = 1.24 y A3=z(1+0.04×8)=1.32zA_3 = z(1 + 0.04 \times 8) = 1.32 z Since the amounts are equal: 1.20x=1.24y=1.32z1.20 x = 1.24 y = 1.32 z Dividing by 0.04\displaystyle 0.04: 30x=31y=33z30 x = 31 y = 33 z **Step 2: Find the ratio of the parts** x:y:z=130:131:133x : y : z = \frac{1}{30} : \frac{1}{31} : \frac{1}{33} Multiplying by 30×31×33=30690\displaystyle 30 \times 31 \times 33 = 30690: x:y:z=1023:990:930x : y : z = 1023 : 990 : 930 Sum of the ratio parts = 1023+990+930=2943\displaystyle 1023 + 990 + 930 = 2943. **Step 3: Calculate the value of each part** x=8829×10232943=3×1023=Rs. 3,069x = 8829 \times \frac{1023}{2943} = 3 \times 1023 = \text{Rs. }3,069 y=8829×9902943=3×990=Rs. 2,970y = 8829 \times \frac{990}{2943} = 3 \times 990 = \text{Rs. }2,970 z=8829×9302943=3×930=Rs. 2,790z = 8829 \times \frac{930}{2943} = 3 \times 930 = \text{Rs. }2,790 Hence, **Option A** 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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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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