Mathematics of FinanceMCQMTP June 24 Series IIQuestion 1414 of 512
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A man invests an amount of $15,860$ in the names of his three sons A, B and C in such a way that they get the same interest after $2,3$ and 4\displaystyle 4 years respectively. If the rate of interest is 5%\displaystyle 5\%, then the ratio of amount invested in the name of A, B and C is.

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

✅ Option a — $6:4:3$

All Options:

  • A$6:4:3$
  • B$3:4:6$
  • C$30:12:5$
  • DNone of these

Detailed Solution & Explanation

Let the amounts invested in the names of A, B, and C be PA\displaystyle P_A, PB\displaystyle P_B, and PC\displaystyle P_C respectively. Given parameters: * Total investment = Rs. 15,860\displaystyle Rs. \displaystyle \text{Rs. }15,860 * Rate of interest (r\displaystyle r) = 5%\displaystyle 5\% p.a. Simple Interest * Times (tA,tB,tC\displaystyle t_A, t_B, t_C) = $2, 3,and\displaystyle and4$ years respectively The simple interests obtained from the three investments are: IA=PA×5×2100=0.10PAI_A = PA×5×2100=0\displaystyle \frac{P_A \times 5 \times 2}{100} = 0.10 P_A IB=PB×5×3100=0.15PBI_B = PB×5×3100=0\displaystyle \frac{P_B \times 5 \times 3}{100} = 0.15 P_B IC=PC×5×4100=0.20PCI_C = PC×5×4100=0\displaystyle \frac{P_C \times 5 \times 4}{100} = 0.20 P_C Since the interests earned are equal: 0.10PA=0.15PB=0.20PC0.10 P_A = 0.15 P_B = 0.20 P_C Dividing the entire relation by $0.05$ (or multiplying by $20$): 2PA=3PB=4PC2 P_A = 3 P_B = 4 P_C Let $2 P_A = 3 P_B = 4 P_C = k$. Then: PA=k2,PB=k3,PC=k4P_A = k2\displaystyle \frac{k}{2}, \quad P_B = k3\displaystyle \frac{k}{3}, \quad P_C = k4\displaystyle \frac{k}{4} The ratio of the investments (PA:PB:PC\displaystyle P_A : P_B : P_C) is: PA:PB:PC=k2:k3:k4P_A : P_B : P_C = k2\displaystyle \frac{k}{2} : k3\displaystyle \frac{k}{3} : k4\displaystyle \frac{k}{4} PA:PB:PC=12:13:14P_A : P_B : P_C = 12\displaystyle \frac{1}{2} : 13\displaystyle \frac{1}{3} : 14\displaystyle \frac{1}{4} Multiplying each term by the LCM of $2, 3,and\displaystyle and4$ (which is $12$): PA:PB:PC=6:4:3P_A : P_B : P_C = 6 : 4 : 3 Thus, the ratio of the amounts invested is $6:4:3$. 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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