Mathematics for FinancePYQ Nov 19Question 1299 of 512
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Certain sum of money borrowed at simple interest amount to Rs.2688\displaystyle 2688 in three years and to 2784\displaystyle 2784 in four years at the rate p.a. equal to.

Options

A7%\displaystyle 7\%
B6%\displaystyle 6\%
C8%\displaystyle 8\%
D4%\displaystyle 4\%
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Correct Answer

✅ Option d — 4%\displaystyle 4\%

All Options:

  • A7%\displaystyle 7\%
  • B6%\displaystyle 6\%
  • C8%\displaystyle 8\%
  • D4%\displaystyle 4\%

Detailed Solution & Explanation

**Derivation of Simple Interest Rate** Given: - Amount in 3\displaystyle 3 years (A3\displaystyle A_3) = Rs. 2,688\displaystyle \text{Rs. }2,688 - Amount in 4\displaystyle 4 years (A4\displaystyle A_4) = Rs. 2,784\displaystyle \text{Rs. }2,784 **Step 1: Find the Simple Interest earned in 1 year (SI1\displaystyle SI_1)** Since simple interest is constant every year: SI1=A4−A3=2784−2688=Rs. 96SI_1 = A_4 - A_3 = 2784 - 2688 = \text{Rs. }96 **Step 2: Solve for the Principal (P\displaystyle P)** P=A3−(3×SI1)P = A_3 - (3 \times SI_1) P=2688−(3×96)=2688−288=Rs. 2,400P = 2688 - (3 \times 96) = 2688 - 288 = \text{Rs. }2,400 **Step 3: Calculate the interest rate (R\displaystyle R)** SI1=P×R×1100SI_1 = \frac{P \times R \times 1}{100} 96=2400×R×110096 = \frac{2400 \times R \times 1}{100} 96=24R  ⟹  R=9624=4% per annum96 = 24 R \implies R = \frac{96}{24} = 4\% \text{ per annum} Hence, **Option D** is the correct answer.

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