Mathematics for FinanceMTP Oct 21, ICAI SMQuestion 1337 of 512
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A sum of money amount to 6,200\displaystyle 6,200 in 2\displaystyle 2 years and 7,400\displaystyle 7,400 in 3\displaystyle 3 years. The principal and rate

Options

A3,800,31.57%\displaystyle 3,800, 31.57\%
B3,000,20%\displaystyle 3,000, 20\%
C3,500,15%\displaystyle 3,500, 15\%
Dnone of these
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Correct Answer

✅ Option a — 3,800,31.57%\displaystyle 3,800, 31.57\%

All Options:

  • A3,800,31.57%\displaystyle 3,800, 31.57\%
  • B3,000,20%\displaystyle 3,000, 20\%
  • C3,500,15%\displaystyle 3,500, 15\%
  • Dnone of these

Detailed Solution & Explanation

**Derivation of Principal and Rate of Simple Interest** Given: - Amount in 2\displaystyle 2 years (A2\displaystyle A_2) = Rs. 6,200\displaystyle \text{Rs. }6,200 - Amount in 3\displaystyle 3 years (A3\displaystyle A_3) = Rs. 7,400\displaystyle \text{Rs. }7,400 **Step 1: Find Simple Interest for 1 year (SI1\displaystyle SI_1)** SI1=A3−A2=7400−6200=Rs. 1,200SI_1 = A_3 - A_2 = 7400 - 6200 = \text{Rs. }1,200 **Step 2: Find the Principal (P\displaystyle P)** P=A2−(2×SI1)=6200−(2×1200)=6200−2400=Rs. 3,800P = A_2 - (2 \times SI_1) = 6200 - (2 \times 1200) = 6200 - 2400 = \text{Rs. }3,800 **Step 3: Calculate the Rate of Interest (R\displaystyle R)** SI1=P×R×1100SI_1 = \frac{P \times R \times 1}{100} 1200=3800×R×11001200 = \frac{3800 \times R \times 1}{100} 1200=38R1200 = 38 R R=120038≈31.578% per annumR = \frac{1200}{38} \approx 31.578\% \text{ per annum} Hence, **Option A** is the correct answer.

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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