Mathematics of FinanceMCQMTP Sep 24 Series IQuestion 1424 of 512
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The simple interest on sum of money at 6%\displaystyle 6\% p.a. for 7\displaystyle 7 years is equal to twice of simple interest on another sum for 9\displaystyle 9 years at 5%\displaystyle 5\% p.a. The ratio will be:

Options

A2:15\displaystyle 2:15
B7:15\displaystyle 7:15
C15:7\displaystyle 15:7
D1:7\displaystyle 1:7
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Correct Answer

Option c15:7\displaystyle 15:7

All Options:

  • A2:15\displaystyle 2:15
  • B7:15\displaystyle 7:15
  • C15:7\displaystyle 15:7
  • D1:7\displaystyle 1:7

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Detailed Solution & Explanation

Let the first sum of money be P1\displaystyle P_1 and the second sum of money be P2\displaystyle P_2. Given parameters: * For the first sum: Rate (r1\displaystyle r_1) = 6%\displaystyle 6\% p.a., Time (t1\displaystyle t_1) = 7\displaystyle 7 years SI1=P1×6×7100=42P1100=0.42P1SI_1 = \frac{P_1 \times 6 \times 7}{100} = \frac{42 P_1}{100} = 0.42 P_1 * For the second sum: Rate (r2\displaystyle r_2) = 5%\displaystyle 5\% p.a., Time (t2\displaystyle t_2) = 9\displaystyle 9 years SI2=P2×5×9100=45P2100=0.45P2SI_2 = \frac{P_2 \times 5 \times 9}{100} = \frac{45 P_2}{100} = 0.45 P_2 We are given that SI1\displaystyle SI_1 is equal to twice of SI2\displaystyle SI_2: SI1=2×SI2SI_1 = 2 \times SI_2 0.42P1=2×(0.45P2)0.42 P_1 = 2 \times (0.45 P_2) 0.42P1=0.90P20.42 P_1 = 0.90 P_2 The ratio of the two sums (P1:P2\displaystyle P_1 : P_2) is: P1P2=0.900.42=9042=157\frac{P_1}{P_2} = \frac{0.90}{0.42} = \frac{90}{42} = \frac{15}{7} Thus, the ratio of the sums is 15:7\displaystyle 15:7. 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.

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