Mathematics for FinancePYQ Nov 18Question 1177 of 512
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If an amount is kept at S. I. it earns an interest of Rs. 600\displaystyle \text{Rs. }600 in first two years but when kept at compound interest it earns an interest of Rs. 660\displaystyle \text{Rs. }660 for the same period, then the rate of interest and principal amount respectively are:

Options

A20%,Rs. 1,200\displaystyle 20\%, \text{Rs. }1,200
B20%,Rs. 1,500\displaystyle 20\%, \text{Rs. }1,500
C10%,Rs. 1,200\displaystyle 10\%, \text{Rs. }1,200
D10%,Rs. 1,500\displaystyle 10\%, \text{Rs. }1,500
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Correct Answer

✅ Option b — 20%,Rs. 1,500\displaystyle 20\%, \text{Rs. }1,500

All Options:

  • A20%,Rs. 1,200\displaystyle 20\%, \text{Rs. }1,200
  • B20%,Rs. 1,500\displaystyle 20\%, \text{Rs. }1,500
  • C10%,Rs. 1,200\displaystyle 10\%, \text{Rs. }1,200
  • D10%,Rs. 1,500\displaystyle 10\%, \text{Rs. }1,500

Detailed Solution & Explanation

**Derivation of Rate and Principal from Simple and Compound Interest** Given: - Simple Interest (SI\displaystyle SI) for 2\displaystyle 2 years = Rs. 600\displaystyle \text{Rs. }600 - Compound Interest (CI\displaystyle CI) for 2\displaystyle 2 years = Rs. 660\displaystyle \text{Rs. }660 **Step 1: Find Simple Interest for 1\displaystyle 1 year** Since Simple Interest is constant every year: SI for 1st year=6002=Rs. 300\text{SI for 1st year} = \frac{600}{2} = \text{Rs. }300 SI for 2nd year=Rs. 300\text{SI for 2nd year} = \text{Rs. }300 **Step 2: Determine the difference between CI and SI** For the first year, SI=CI=Rs. 300\displaystyle SI = CI = \text{Rs. }300. The difference in the interest in the second year is due to the interest earned on the first year's interest. Difference=CI−SI=660−600=Rs. 60\text{Difference} = CI - SI = 660 - 600 = \text{Rs. }60 This Rs. 60\displaystyle \text{Rs. }60 is the interest earned on Rs. 300\displaystyle \text{Rs. }300 (the first year's interest) for 1\displaystyle 1 year. **Step 3: Calculate the Rate of Interest (R\displaystyle R)** Interest=Principal×R×T100\text{Interest} = \frac{\text{Principal} \times R \times T}{100} 60=300×R×110060 = \frac{300 \times R \times 1}{100} 60=3R  ⟹  R=20% per annum60 = 3R \implies R = 20\% \text{ per annum} **Step 4: Calculate the Principal Amount (P\displaystyle P)** Using the Simple Interest of the first year: SI for 1st year=P×R×1100\text{SI for 1st year} = \frac{P \times R \times 1}{100} 300=P×20×1100300 = \frac{P \times 20 \times 1}{100} 300=P5  ⟹  P=Rs. 1,500300 = \frac{P}{5} \implies P = \text{Rs. }1,500 Hence, **Option B** is the correct answer.

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