Mathematics of FinanceMCQMTP Jun 23 Series IIQuestion 1382 of 512
All Questions

Mrs. Sudha lent 4,000\displaystyle 4,000 in such a way that some amount to Mr. A at 3%\displaystyle 3\% p.a. S.I. and rest amount 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
For any discrepancies in this question, email contact@cadada.in

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

Ad

Detailed Solution & Explanation

**Derivation of Amount Lent to Mr. A** Given: - Total sum lent = Rs. 4,000\displaystyle \text{Rs. }4,000 - Rate of simple interest for Mr. A = 3%\displaystyle 3\% p.a. - Rate of simple interest for B = 5%\displaystyle 5\% p.a. - Total annual interest received = Rs. 144\displaystyle \text{Rs. }144 **Step 1: Set up the variables** Let x\displaystyle x be the amount lent to Mr. A. Then, the amount lent to B is (4000x)\displaystyle (4000 - x). **Step 2: Formulate and solve the annual interest equation** 0.03x+0.05(4000x)=1440.03 x + 0.05(4000 - x) = 144 0.03x+2000.05x=1440.03 x + 200 - 0.05 x = 144 0.02x=144200-0.02 x = 144 - 200 0.02x=56-0.02 x = -56 x=560.02=Rs. 2,800x = \frac{56}{0.02} = \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

Exam Strategy Tip

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.

Related Comparison Tables

More Questions from Mathematics of Finance

Ready to Master Mathematics of Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free