Mathematics for FinanceMTP Dec 23 Series IQuestion 1388 of 512
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If the difference between C.I. and S.I on a certain sum of money at 5%\displaystyle 5\% p.a. for 2\displaystyle 2 years is 1.50\displaystyle 1.50. Find the sum of money

Options

A600\displaystyle 600
B500\displaystyle 500
C400\displaystyle 400
DNone of these
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Correct Answer

✅ Option a — 600\displaystyle 600

All Options:

  • A600\displaystyle 600
  • B500\displaystyle 500
  • C400\displaystyle 400
  • DNone of these

Detailed Solution & Explanation

**Derivation of Principal Sum** Given: - Time (t\displaystyle t) = 2\displaystyle 2 years - Rate (r\displaystyle r) = 5%\displaystyle 5\% per annum - Difference between Compound Interest and Simple Interest (CI−SI\displaystyle CI - SI) = Rs. 1.50\displaystyle \text{Rs. }1.50 **Step 1: Use the difference formula for 2 years** Difference=P(r100)2\text{Difference} = P \left(\frac{r}{100}\right)^2 1.50=P(5100)21.50 = P \left(\frac{5}{100}\right)^2 1.50=P(0.05)21.50 = P (0.05)^2 1.50=0.0025P1.50 = 0.0025 P **Step 2: Solve for P\displaystyle P** P=1.500.0025=Rs. 600P = \frac{1.50}{0.0025} = \text{Rs. }600 Hence, **Option A** is the correct answer.

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