What is the ratio of simple interest earned on certain amount at the rate of `12%` p.a for 9 years and that for 12 years ?

A. `1:2`

B `2:3`

C. 3:4

D. `4:5`

Options

A. C
B. D
C. B
D. A

Answer

To find the ratio of simple interest earned on a certain amount at the rate of 12% per annum for 9 years and for 12 years, we can follow these steps:

### Step 1: Understand the formula for Simple Interest
The formula for calculating Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (the initial amount of money)
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 2: Calculate Simple Interest for 9 years
Let’s denote the principal amount as \( P \).

Using the formula for SI:
\[ SI_{9} = \frac{P \times 12 \times 9}{100} \]
\[ SI_{9} = \frac{P \times 108}{100} = \frac{108P}{100} \]

### Step 3: Calculate Simple Interest for 12 years
Now, we calculate the Simple Interest for 12 years:
\[ SI_{12} = \frac{P \times 12 \times 12}{100} \]
\[ SI_{12} = \frac{P \times 144}{100} = \frac{144P}{100} \]

### Step 4: Find the ratio of SI for 9 years to SI for 12 years
Now we need to find the ratio of \( SI_{9} \) to \( SI_{12} \):
\[ \text{Ratio} = \frac{SI_{9}}{SI_{12}} = \frac{\frac{108P}{100}}{\frac{144P}{100}} \]
The \( P \) and \( 100 \) cancel out:
\[ \text{Ratio} = \frac{108}{144} \]

### Step 5: Simplify the ratio
To simplify \( \frac{108}{144} \):
\[ \frac{108 \div 36}{144 \div 36} = \frac{3}{4} \]

### Conclusion
Thus, the ratio of simple interest earned for 9 years to that for 12 years is:
\[ \text{Ratio} = 3:4 \]

### Final Answer
The correct option is **C. 3:4**.

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