In what time will the simple interest on Rs 900 at 6 % be equal to the interest on Rs 540 for 8 years at 5 % ?

Options

A. a. 4 Years
B. b. 6 Years
C. c. 8 Years
D. d. 10 Years

Answer

To solve the problem step by step, we need to find the time (T) when the simple interest on Rs 900 at 6% will equal the interest on Rs 540 for 8 years at 5%.

### Step 1: Calculate the interest on Rs 540 for 8 years at 5%
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount
- \(R\) = Rate of interest
- \(T\) = Time in years

For Rs 540 at 5% for 8 years:
\[ SI = \frac{540 \times 5 \times 8}{100} \]

### Step 2: Calculate the interest
\[ SI = \frac{540 \times 5 \times 8}{100} = \frac{21600}{100} = 216 \]

### Step 3: Set up the equation for the interest on Rs 900 at 6%
Now, we need to find the time \(T\) when the interest on Rs 900 at 6% is equal to Rs 216.
Using the simple interest formula:
\[ SI = \frac{P \times R \times T}{100} \]
For Rs 900 at 6%:
\[ 216 = \frac{900 \times 6 \times T}{100} \]

### Step 4: Rearranging the equation
Rearranging the equation to solve for \(T\):
\[ 216 = \frac{5400T}{100} \]
\[ 216 = 54T \]

### Step 5: Solve for \(T\)
Now, divide both sides by 54:
\[ T = \frac{216}{54} = 4 \]

### Conclusion
The time \(T\) is 4 years.