Mathematics for FinanceMTP June 22Question 1356 of 512
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The rate of interest for the first 2\displaystyle 2 year is 3%\displaystyle 3\% per annum, for next 3\displaystyle 3 years is 8%\displaystyle 8\% per annum and for the period beyond 5\displaystyle 5 years, 10%\displaystyle 10\% per annum. If a man gets 1520\displaystyle 1520 as a simple interest for 6\displaystyle 6 years, how much money did he deposit?

Options

A3800\displaystyle 3800
B3000\displaystyle 3000
C4000\displaystyle 4000
DNone of these
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Correct Answer

✅ Option a — 3800\displaystyle 3800

All Options:

  • A3800\displaystyle 3800
  • B3000\displaystyle 3000
  • C4000\displaystyle 4000
  • DNone of these

Detailed Solution & Explanation

**Derivation of Principal Sum** Given: - Total Simple Interest received (SI\displaystyle SI) = Rs. 1,520\displaystyle \text{Rs. }1,520 for t=6\displaystyle t = 6 years - Rate structure: - For first 2\displaystyle 2 years: r1=3%\displaystyle r_1 = 3\% per annum - For next 3\displaystyle 3 years: r2=8%\displaystyle r_2 = 8\% per annum - For the period beyond 5\displaystyle 5 years (which is 1\displaystyle 1 year in this case): r3=10%\displaystyle r_3 = 10\% per annum **Step 1: Calculate the total cumulative interest percentage** Total R×T=(2×3%)+(3×8%)+(1×10%)=6%+24%+10%=40%\text{Total } R \times T = (2 \times 3\%) + (3 \times 8\%) + (1 \times 10\%)= 6\% + 24\% + 10\% = 40\% **Step 2: Set up simple interest formula and solve for Principal (P\displaystyle P)** SI=P×Total R×T100SI = P \times \frac{\text{Total } R \times T}{100} 1520=P×0.401520 = P \times 0.40 P=15200.40=Rs. 3,800P = \frac{1520}{0.40} = \text{Rs. }3,800 *(Note: The database lists Option B (3,000\displaystyle 3,000) as correct, which is mathematically incorrect. The correct principal is 3,800, which is Option A.)* Hence, **Option A** is the correct answer.

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