what will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 8 years ?

Options

A. `1:3`
B. `2:3`
C. `1:4`
D. `3:4`

Answer

To find the ratio of simple interest earned on a certain amount at the same rate of interest for 6 years and for 8 years, we can follow these steps:

### Step 1: Write 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 per annum
- \( T \) = Time in years

### Step 2: Calculate Simple Interest for 6 years
Using the formula, the Simple Interest for 6 years can be calculated as:
\[ SI_{6} = \frac{P \times R \times 6}{100} \]

### Step 3: Calculate Simple Interest for 8 years
Similarly, the Simple Interest for 8 years can be calculated as:
\[ SI_{8} = \frac{P \times R \times 8}{100} \]

### Step 4: Form the ratio of Simple Interest for 6 years to that for 8 years
Now, we can form the ratio of the Simple Interest for 6 years to the Simple Interest for 8 years:
\[ \text{Ratio} = \frac{SI_{6}}{SI_{8}} = \frac{\frac{P \times R \times 6}{100}}{\frac{P \times R \times 8}{100}} \]

### Step 5: Simplify the ratio
When we simplify the ratio, the \( P \), \( R \), and \( 100 \) cancel out:
\[ \text{Ratio} = \frac{6}{8} \]

### Step 6: Further simplify the ratio
Now, we can simplify \( \frac{6}{8} \):
\[ \text{Ratio} = \frac{3}{4} \]

### Final Answer
The ratio of the simple interest earned for 6 years to that for 8 years is:
\[ \text{Ratio} = 3 : 4 \]

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