Mathematics for FinancePYQ July 21Question 1225 of 512
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A certain sum amounts to 15,748\displaystyle 15,748 in 3\displaystyle 3 years at simple interest at 1%\displaystyle 1\% p.a. The same sum amounts to 16,510\displaystyle 16,510 at r+2%\displaystyle r+2\% p.a. SI in the same time. What is the value of r\displaystyle r?

Options

A10%\displaystyle 10\%
B8%\displaystyle 8\%
C12%\displaystyle 12\%
D6%\displaystyle 6\%
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Correct Answer

✅ Option b — 8%\displaystyle 8\%

All Options:

  • A10%\displaystyle 10\%
  • B8%\displaystyle 8\%
  • C12%\displaystyle 12\%
  • D6%\displaystyle 6\%

Detailed Solution & Explanation

**Derivation of Rate of Simple Interest** Given: - Amount at r%\displaystyle r\% simple interest in 3\displaystyle 3 years (A1\displaystyle A_1) = Rs. 15,748\displaystyle \text{Rs. }15,748 - Amount at (r+2)%\displaystyle (r+2)\% simple interest in 3\displaystyle 3 years (A2\displaystyle A_2) = Rs. 16,510\displaystyle \text{Rs. }16,510 **Step 1: Express the difference in amounts** The difference in the two amounts is due to the additional simple interest earned from the increase in rate by 2%\displaystyle 2\%. Additional Simple Interest=A2−A1=16510−15748=Rs. 762\text{Additional Simple Interest} = A_2 - A_1 = 16510 - 15748 = \text{Rs. }762 **Step 2: Find the Principal (P\displaystyle P) using the additional simple interest** Additional SI=P×Additional Rate×t100\text{Additional SI} = \frac{P \times \text{Additional Rate} \times t}{100} 762=P×2×3100762 = \frac{P \times 2 \times 3}{100} 762=6P100762 = \frac{6P}{100} 6P=76200  ⟹  P=Rs. 12,7006P = 76200 \implies P = \text{Rs. }12,700 **Step 3: Solve for the rate of interest (r\displaystyle r)** Using the simple interest earned in the first case: SI1=A1−P=15748−12700=Rs. 3,048SI_1 = A_1 - P = 15748 - 12700 = \text{Rs. }3,048 SI1=P×r×t100SI_1 = \frac{P \times r \times t}{100} 3048=12700×r×31003048 = \frac{12700 \times r \times 3}{100} 3048=381r  ⟹  r=3048381=8% per annum3048 = 381 r \implies r = \frac{3048}{381} = 8\% \text{ per annum} Hence, **Option B** is the correct answer.

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