Mathematics for FinanceMTP 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 a — 2,800\displaystyle 2,800

All Options:

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

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 4,000−x\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+(4,000−x)×5×1100=144\frac{x \times 3 \times 1}{100} + \frac{(4,000 - x) \times 5 \times 1}{100} = 144 0.03x+0.05(4,000−x)=1440.03x + 0.05(4,000 - x) = 144 0.03x+200−0.05x=1440.03x + 200 - 0.05x = 144 200−0.02x=144200 - 0.02x = 144 Solving for x\displaystyle x: 0.02x=200−144=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.

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