Mathematics for FinancePYQ Nov 19Question 1294 of 512
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A person deposited a sum of 10,000\displaystyle 10,000 in a bank. After 2\displaystyle 2 years, he withdrew 4,000\displaystyle 4,000 and at the end of 5\displaystyle 5 years, he received an amount of 7,900\displaystyle 7,900; then the rate of simple interest is:

Options

A6%\displaystyle 6\%
B5%\displaystyle 5\%
C10%\displaystyle 10\%
DNone of these
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Correct Answer

✅ Option b — 5%\displaystyle 5\%

All Options:

  • A6%\displaystyle 6\%
  • B5%\displaystyle 5\%
  • C10%\displaystyle 10\%
  • DNone of these

Detailed Solution & Explanation

**Derivation of Simple Interest Rate** Given: - Initial Principal (P\displaystyle P) = Rs. 10,000\displaystyle \text{Rs. }10,000 - At t=2\displaystyle t=2 years, withdrawal = Rs. 4,000\displaystyle \text{Rs. }4,000, leaving a new principal of Rs. 6,000\displaystyle \text{Rs. }6,000 for the remaining 3\displaystyle 3 years. - Total amount received at t=5\displaystyle t=5 years = Rs. 7,900\displaystyle \text{Rs. }7,900 **Step 1: Set up interest equations for both periods** - Interest for first 2 years: I1=10000×R×2100=200RI_1 = \frac{10000 \times R \times 2}{100} = 200 R - Interest for the remaining 3 years: I2=6000×R×3100=180RI_2 = \frac{6000 \times R \times 3}{100} = 180 R - Total simple interest earned over 5 years: Total Interest=I1+I2=380R\text{Total Interest} = I_1 + I_2 = 380 R **Step 2: Determine total interest earned from cash flows** The total money received/withdrawn by the person is 4,000+7,900=Rs. 11,900\displaystyle 4,000 + 7,900 = \text{Rs. }11,900. Since the initial deposit was 10,000\displaystyle 10,000: Total Interest Earned=11900−10000=Rs. 1,900\text{Total Interest Earned} = 11900 - 10000 = \text{Rs. }1,900 **Step 3: Solve for Rate (R\displaystyle R)** 380R=1900380 R = 1900 R=1900380=5% per annumR = \frac{1900}{380} = 5\% \text{ per annum} Hence, **Option B** is the correct answer.

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