Mathematics for FinancePYQ Nov 20Question 1210 of 512
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What sum of money will produce 42,800\displaystyle 42,800 as an interest in 3\displaystyle 3 years and 3\displaystyle 3 months at 2.5%\displaystyle 2.5\% p.a. simple interest?

Options

A3,75,000\displaystyle 3,75,000
B5,26,769\displaystyle 5,26,769
C4,22,000\displaystyle 4,22,000
D2,24,000\displaystyle 2,24,000
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Correct Answer

✅ Option b — 5,26,769\displaystyle 5,26,769

All Options:

  • A3,75,000\displaystyle 3,75,000
  • B5,26,769\displaystyle 5,26,769
  • C4,22,000\displaystyle 4,22,000
  • D2,24,000\displaystyle 2,24,000

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Simple Interest (SI\displaystyle SI) = Rs. 42,800\displaystyle \text{Rs. }42,800 - Time (t\displaystyle t) = 3\displaystyle 3 years and 3\displaystyle 3 months = 3+312=3.25\displaystyle 3 + \frac{3}{12} = 3.25 years - Rate of Interest (r\displaystyle r) = 2.5%\displaystyle 2.5\% per annum **Step 1: Set up the Simple Interest equation** SI=P×r×t100SI = \frac{P \times r \times t}{100} 42800=P×2.5×3.2510042800 = \frac{P \times 2.5 \times 3.25}{100} 42800=P×8.12510042800 = \frac{P \times 8.125}{100} **Step 2: Solve for P\displaystyle P** 42800×100=8.125P42800 \times 100 = 8.125 P 4280000=8.125P4280000 = 8.125 P P=42800008.125≈Rs. 5,26,769.23P = \frac{4280000}{8.125} \approx \text{Rs. }5,26,769.23 Hence, **Option B** is the correct answer.

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