Mathematics for FinanceMTP Dec 23 Series IIQuestion 1401 of 512
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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Options

A4,000\displaystyle 4,000
B5,000\displaystyle 5,000
C6,000\displaystyle 6,000
DNone of these
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Correct Answer

✅ Option b — 5,000\displaystyle 5,000

All Options:

  • A4,000\displaystyle 4,000
  • B5,000\displaystyle 5,000
  • C6,000\displaystyle 6,000
  • DNone of these

Detailed Solution & Explanation

**Derivation of Principal Sum** Given: - Time (t\displaystyle t) = 2.5\displaystyle 2.5 years - Let the original rate be R\displaystyle R. - If rate increases by 4%\displaystyle 4\%, interest increases by Rs. 500\displaystyle \text{Rs. }500. **Step 1: Express the interest difference** Interest Difference=P×(R+4)×t100−P×R×t100\text{Interest Difference} = \frac{P \times (R + 4) \times t}{100} - \frac{P \times R \times t}{100} 500=P×4×t100500 = \frac{P \times 4 \times t}{100} 500=P×4×2.5100500 = \frac{P \times 4 \times 2.5}{100} 500=10P100500 = \frac{10 P}{100} 500=0.10P500 = 0.10 P **Step 2: Solve for P\displaystyle P** P=5000.10=Rs. 5,000P = \frac{500}{0.10} = \text{Rs. }5,000 Hence, **Option B** is the correct answer.

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