Mathematics for FinanceMTP Dec 22 Series IIQuestion 1375 of 512
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Mr. X lent some amount of money at 4%\displaystyle 4\% S.I. and he obtained 520\displaystyle 520 less than he lent in 5\displaystyle 5 years. The sum lent is

Options

A650\displaystyle 650
B750\displaystyle 750
C620\displaystyle 620
Dnone of these
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Correct Answer

✅ Option a — 650\displaystyle 650

All Options:

  • A650\displaystyle 650
  • B750\displaystyle 750
  • C620\displaystyle 620
  • Dnone of these

Detailed Solution & Explanation

**Derivation of Sum Lent** Given: - Rate of simple interest (R\displaystyle R) = 4%\displaystyle 4\% per annum - Time (T\displaystyle T) = 5\displaystyle 5 years - Interest obtained is Rs. 520\displaystyle \text{Rs. }520 less than the principal (SI=P−520\displaystyle SI = P - 520) **Step 1: Set up the Simple Interest equation** SI=P×R×T100SI = \frac{P \times R \times T}{100} P−520=P×4×5100P - 520 = \frac{P \times 4 \times 5}{100} P−520=0.20PP - 520 = 0.20 P **Step 2: Solve for P\displaystyle P** P−0.20P=520P - 0.20 P = 520 0.80P=5200.80 P = 520 P=5200.80=Rs. 650P = \frac{520}{0.80} = \text{Rs. }650 *(Note: The database lists Option B (750\displaystyle 750) as correct, which is a typo in the key. The mathematically correct sum lent is 650, which is Option A.)* 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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