If amount of Rs 14000 becomes 35000 in 6 years then find the rate of interest?

Options

A. `30%`
B. `20%`
C. `18%`
D. `25%`

Answer

To find the rate of interest when an amount of Rs 14,000 becomes Rs 35,000 in 6 years, we can follow these steps:

### Step 1: Identify the Principal and Amount
- Principal (P) = Rs 14,000
- Amount (A) = Rs 35,000

### Step 2: Calculate the Simple Interest (SI)
- Simple Interest (SI) can be calculated using the formula:
\[ SI = A - P \]
- Substituting the values:
\[ SI = 35,000 - 14,000 = 21,000 \]

### Step 3: Use the Simple Interest Formula
- The formula for Simple Interest is:
\[ SI = \frac{P \times r \times t}{100} \]
- Where:
- \( P \) = Principal
- \( r \) = Rate of Interest
- \( t \) = Time in years

### Step 4: Substitute Known Values
- We know:
- \( SI = 21,000 \)
- \( P = 14,000 \)
- \( t = 6 \) years
- Substituting these values into the formula:
\[ 21,000 = \frac{14,000 \times r \times 6}{100} \]

### Step 5: Simplify the Equation
- Rearranging the equation to solve for \( r \):
\[ 21,000 = \frac{84,000r}{100} \]
- Multiplying both sides by 100 to eliminate the fraction:
\[ 2,100,000 = 84,000r \]

### Step 6: Solve for \( r \)
- Dividing both sides by 84,000:
\[ r = \frac{2,100,000}{84,000} \]
- Simplifying the fraction:
\[ r = 25 \]

### Conclusion
- The rate of interest \( r \) is 25%.