Simple interest on a sum of Rs 1400 for 3 years and 4 months is Rs 700. What is the rate (in percentage) of interest per annum?

Options

A. 17
B. 15
C. 18
D. 12

Answer

To find the rate of interest per annum, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 1400
- Simple Interest (SI) = Rs. 700
- Time (T) = 3 years and 4 months

### Step 2: Convert the time into years
- 4 months can be converted into years by dividing by 12.
- \( T = 3 + \frac{4}{12} = 3 + \frac{1}{3} = \frac{10}{3} \) years

### Step 3: Use the formula for Simple 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 (per annum)
- T = Time (in years)

### Step 4: Substitute the known values into the formula
Substituting the values we have:
\[ 700 = \frac{1400 \times R \times \frac{10}{3}}{100} \]

### Step 5: Simplify the equation
Multiply both sides by 100 to eliminate the fraction:
\[ 700 \times 100 = 1400 \times R \times \frac{10}{3} \]
\[ 70000 = \frac{14000R}{3} \]

### Step 6: Multiply both sides by 3 to eliminate the denominator
\[ 70000 \times 3 = 14000R \]
\[ 210000 = 14000R \]

### Step 7: Solve for R
Now, divide both sides by 14000:
\[ R = \frac{210000}{14000} \]
\[ R = 15 \]

### Step 8: State the final answer
The rate of interest per annum is \( R = 15\% \).