At the certain rate of simple interest, a certain sum doubles itself in 10 years. It will treble itself in-

Options

A. 15 years
B. 20 years
C. 30 years
D. 12 years

Answer

To solve the problem, we need to determine how long it will take for a certain sum of money to triple itself at the same rate of simple interest that causes it to double in 10 years.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that a certain sum doubles in 10 years. We need to find out how long it will take for the same sum to triple.

2. **Using the Formula for Simple Interest**:
We can use the relationship between the time taken to double and triple the amount using the formula:
\[ \frac{N_1 - 1}{T_1} = \frac{N_2 - 1}{T_2} \]
where:
- \(N_1\) is the factor by which the sum doubles (which is 2),
- \(T_1\) is the time taken to double (which is 10 years),
- \(N_2\) is the factor by which the sum triples (which is 3),
- \(T_2\) is the time taken to triple (which we need to find).

3. **Substituting Values**:
Substitute the known values into the formula:
\[ \frac{2 - 1}{10} = \frac{3 - 1}{T_2} \]
This simplifies to:
\[ \frac{1}{10} = \frac{2}{T_2} \]

4. **Cross Multiplying**:
Now, cross-multiply to solve for \(T_2\):
\[ 1 \cdot T_2 = 2 \cdot 10 \]
Which gives:
\[ T_2 = 20 \]

5. **Conclusion**:
Therefore, it will take 20 years for the sum to triple itself.

### Final Answer:
The time taken for the sum to treble itself is **20 years**.

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