How much time will it take for an amount of ₹360 to yield ₹72 as interest at 5% p.a. of simple interest?

Options

A. 3 years
B. 4 years
C. 2.5 years
D. 3.5 years

Answer

To solve the problem of how much time it will take for an amount of ₹360 to yield ₹72 as interest at a rate of 5% per annum using simple interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = ₹360
- Simple Interest (SI) = ₹72
- Rate of Interest (R) = 5% per annum

### Step 2: Use the formula for Simple Interest
The formula for calculating Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal amount
- R = Rate of interest per annum
- T = Time in years

### Step 3: Substitute the known values into the formula
We need to find the time (T), so we rearrange the formula to solve for T:
\[ T = \frac{SI \times 100}{P \times R} \]
Now substituting the known values:
\[ T = \frac{72 \times 100}{360 \times 5} \]

### Step 4: Calculate the denominator
First, calculate the denominator:
\[ 360 \times 5 = 1800 \]

### Step 5: Substitute the denominator back into the equation
Now we substitute back into the equation for T:
\[ T = \frac{72 \times 100}{1800} \]

### Step 6: Calculate the numerator
Calculate the numerator:
\[ 72 \times 100 = 7200 \]

### Step 7: Divide the numerator by the denominator
Now, divide the numerator by the denominator:
\[ T = \frac{7200}{1800} = 4 \]

### Step 8: State the final answer
Thus, the time it will take for ₹360 to yield ₹72 as interest at 5% per annum is:
\[ T = 4 \text{ years} \]