Rs. 6000 amounts to Rs . 7986 in 3 years at Cl. The rate of interest is :

Options

A. `20%`
B. `10%`
C. `15%`
D. `20%`

Answer

To find the rate of interest when Rs. 6000 amounts to Rs. 7986 in 3 years at compound interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs. 6000
- Amount (A) = Rs. 7986
- Time (T) = 3 years

2. **Use the Compound Interest Formula:**
The formula for the amount in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^T \]
where \( r \) is the rate of interest.

3. **Substitute the Known Values:**
Substitute the values of A, P, and T into the formula:
\[ 7986 = 6000 \left(1 + \frac{r}{100}\right)^3 \]

4. **Divide Both Sides by 6000:**
To isolate the term with \( r \):
\[ \frac{7986}{6000} = \left(1 + \frac{r}{100}\right)^3 \]
Calculate \( \frac{7986}{6000} \):
\[ \frac{7986}{6000} = 1.331 \]

5. **Take the Cube Root:**
To solve for \( 1 + \frac{r}{100} \), take the cube root of both sides:
\[ 1 + \frac{r}{100} = \sqrt[3]{1.331} \]
The cube root of 1.331 is approximately 1.1 (since \( 1.1^3 = 1.331 \)).

6. **Isolate \( r \):**
Now, subtract 1 from both sides:
\[ \frac{r}{100} = 1.1 - 1 = 0.1 \]
Multiply both sides by 100 to find \( r \):
\[ r = 0.1 \times 100 = 10 \]

7. **Conclusion:**
The rate of interest \( r \) is 10%.

### Final Answer:
The rate of interest is **10%**.