If the simple interest for 4 year on the amount of 6000 is 1500 then find the rate of interest?

Options

A. `6(1)/(4)%`
B. `10(1)/(4)%`
C. `8(1)/(2)`
D. `9(1)/(3)%`

Answer

To find the rate of interest when the simple interest for 4 years on an amount of 6000 is 1500, we can follow these steps:

### Step 1: Understand the given information
We know:
- Principal (P) = 6000
- Simple Interest (SI) for 4 years = 1500
- Time (T) = 4 years

### Step 2: Calculate the Simple Interest for 1 year
To find the simple interest for 1 year, we divide the total simple interest by the number of years.

\[ \text{SI for 1 year} = \frac{\text{Total SI}}{\text{Time}} = \frac{1500}{4} = 375 \]

### Step 3: Use the formula for Simple Interest to find the Rate of Interest
The formula for Simple Interest is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- SI = Simple Interest
- P = Principal
- R = Rate of Interest
- T = Time in years

We can rearrange this formula to find the rate of interest (R):

\[ R = \frac{SI \times 100}{P \times T} \]

### Step 4: Substitute the values into the formula
Now, substituting the values we have:

\[ R = \frac{375 \times 100}{6000 \times 1} = \frac{37500}{6000} \]

### Step 5: Simplify the fraction
Now we simplify \(\frac{37500}{6000}\):

\[ R = \frac{37500 \div 75}{6000 \div 75} = \frac{500}{80} = \frac{25}{4} \]

### Step 6: Convert to percentage
To convert \(\frac{25}{4}\) into a percentage, we can divide:

\[ \frac{25}{4} = 6.25 \]

Thus, the rate of interest (R) is:

\[ R = 6.25\% \]

### Final Answer
The rate of interest is **6.25%**.

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