In a certain time, the ratio of a certain principal and the simple interset obtained from it are in the ratio 10 : 3 at 10% interset per annum. The number of years the money was invested is

Options

A. 1 year
B. 3 year
C. 5 years
D. 7 years

Answer

To solve the problem step by step, we will follow the information given and use the formula for simple interest.

### Step 1: Understand the given ratio
We know that the ratio of the principal (P) to the simple interest (SI) is given as 10:3. This means we can express the principal and interest in terms of a variable:
- Let the principal be \( P = 10x \)
- Let the simple interest be \( SI = 3x \)

### Step 2: Use the formula for Simple Interest
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) is the simple interest
- \( P \) is the principal
- \( R \) is the rate of interest (10% per annum in this case)
- \( T \) is the time in years

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ 3x = \frac{10x \times 10 \times T}{100} \]

### Step 4: Simplify the equation
Now, we can simplify the equation:
\[ 3x = \frac{100x \times T}{100} \]
This simplifies to:
\[ 3x = 10x \times T \]

### Step 5: Solve for T
To isolate \( T \), we can divide both sides by \( 10x \):
\[ T = \frac{3x}{10x} \]
This simplifies to:
\[ T = \frac{3}{10} \]

### Step 6: Convert T to years
Since the ratio of principal to interest is given, we can conclude that the time \( T \) in years is:
\[ T = 3 \text{ years} \]

### Final Answer
The number of years the money was invested is **3 years**.

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