Question

A sum of money at simple interest doubles in 7 years. It will become four times in

• A. 18 years
• B. 21 years
• C. 38 years
• D. 42 years

Hint:

To double: $SI = 1P$ takes 7 years. To become 4 times: $SI = 3P$ takes $3 \times 7 = 21$ years.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Under simple interest, the interest accrued is directly proportional to time.

Step 2: Key Formula or Approach:
Let principal be $P$.
- When the sum doubles ($A = 2P$), the simple interest earned is $SI_1 = 2P - P = P$ in $T_1 = 7\,\text{years}$.
- For the sum to become four times ($A = 4P$), the simple interest required is $SI_2 = 4P - P = 3P$.

Step 3: Detailed Explanation:
Since $SI \propto T$:
\[\frac{SI_2}{SI_1} = \frac{T_2}{T_1} \implies \frac{3P}{P} = \frac{T_2}{7} \implies T_2 = 3 \times 7 = 21\,\text{years}\]

Step 4: Final Answer:
Hence, the sum will become four times in 21 years.