Mathematics of FinanceMCQMTP Dec 23 Series IIQuestion 3952 of 512
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Miss Liza lent 4,000\displaystyle 4,000 in such a way that some amount was given to Mr. A at 3%\displaystyle 3\% p.a. S.I. and rest amount to was given to B at 5%\displaystyle 5\% p.a. S.I., the annual interest from both is 144\displaystyle 144. Find the amount lent to Mr. A.

Options

A2,800\displaystyle 2,800
B1,200\displaystyle 1,200
C2,500\displaystyle 2,500
DNone of these
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Correct Answer

Option a2,800\displaystyle 2,800

All Options:

  • A2,800\displaystyle 2,800
  • B1,200\displaystyle 1,200
  • C2,500\displaystyle 2,500
  • DNone of these

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Detailed Solution & Explanation

Let the amount lent to Mr. A be x\displaystyle x. Since the total amount lent is Rs. 4,000\displaystyle \text{Rs. }4,000, the amount lent to Mr. B is 4,000x\displaystyle 4,000 - x. Given parameters: * Rate of simple interest for A (rA\displaystyle r_A) = 3%\displaystyle 3\% p.a. * Rate of simple interest for B (rB\displaystyle r_B) = 5%\displaystyle 5\% p.a. * Total annual interest = Rs. 144\displaystyle \text{Rs. }144 * Time (t\displaystyle t) = 1\displaystyle 1 year The sum of the interests from both investments equals the total interest: SIA+SIB=144SI_A + SI_B = 144 x×3×1100+(4,000x)×5×1100=144\frac{x \times 3 \times 1}{100} + \frac{(4,000 - x) \times 5 \times 1}{100} = 144 0.03x+0.05(4,000x)=1440.03x + 0.05(4,000 - x) = 144 0.03x+2000.05x=1440.03x + 200 - 0.05x = 144 2000.02x=144200 - 0.02x = 144 Solving for x\displaystyle x: 0.02x=200144=560.02x = 200 - 144 = 56 x=560.02=2,800x = \frac{56}{0.02} = 2,800 Thus, the amount lent to Mr. A is Rs. 2,800\displaystyle \text{Rs. }2,800. 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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