Mathematics for FinancePYQ Nov 18Question 1281 of 512
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A Sum of money doubles itself in 10\displaystyle 10 years. The number of years it would be trebled itself is:

Options

A25\displaystyle 25 years
B15\displaystyle 15 years
C20\displaystyle 20 years
DNone of these
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Correct Answer

✅ Option c — 20\displaystyle 20 years

All Options:

  • A25\displaystyle 25 years
  • B15\displaystyle 15 years
  • C20\displaystyle 20 years
  • DNone of these

Detailed Solution & Explanation

**Derivation of Time to Treble Sum under Simple Interest** Given: - A sum of money doubles itself in 10\displaystyle 10 years under Simple Interest. **Step 1: Find the rate of interest (r\displaystyle r)** If the sum doubles, the interest earned equals the principal (SI=P\displaystyle SI = P). SI=P×r×t100SI = \frac{P \times r \times t}{100} P=P×r×10100P = \frac{P \times r \times 10}{100} 1=r10  ⟹  r=10% per annum1 = \frac{r}{10} \implies r = 10\% \text{ per annum} **Step 2: Find time (t2\displaystyle t_2) to treble the sum (A=3P\displaystyle A = 3P)** The required simple interest is: SI2=A−P=3P−P=2PSI_2 = A - P = 3P - P = 2P Using the Simple Interest formula: 2P=P×10×t21002P = \frac{P \times 10 \times t_2}{100} 2=t210  ⟹  t2=20 years2 = \frac{t_2}{10} \implies t_2 = 20 \text{ years} Hence, **Option C** 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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