The simple interest on a certain sum of money at the rate of 8% p.a. for 9 years is Rs2880. At what rate of interest can the same amount of simple interest be received on the same sum in 6years?

Options

A. A)12%
B. B)10.5%
C. C)10%
D. D)14%

Answer

To solve the problem step by step, we will use the formula for simple interest:

**Simple Interest (SI) = (Principal * Rate * Time) / 100**

### Step 1: Identify the known values
From the problem, we know:
- The simple interest (SI) for the first case is Rs. 2880.
- The rate of interest (R1) for the first case is 8% per annum.
- The time (T1) for the first case is 9 years.

### Step 2: Use the formula to find the principal (P)
Using the simple interest formula for the first case:

\[ SI = \frac{P \cdot R1 \cdot T1}{100} \]

Substituting the known values:

\[ 2880 = \frac{P \cdot 8 \cdot 9}{100} \]

### Step 3: Simplify and solve for P
First, simplify the equation:

\[ 2880 = \frac{72P}{100} \]

Multiply both sides by 100 to eliminate the fraction:

\[ 288000 = 72P \]

Now, divide both sides by 72 to find P:

\[ P = \frac{288000}{72} = 4000 \]

### Step 4: Set up the equation for the second case
Now, we need to find the rate of interest (R2) for the same principal (P) over a different time (T2 = 6 years) to receive the same simple interest (SI = Rs. 2880).

Using the simple interest formula again:

\[ 2880 = \frac{P \cdot R2 \cdot T2}{100} \]

Substituting the known values:

\[ 2880 = \frac{4000 \cdot R2 \cdot 6}{100} \]

### Step 5: Simplify and solve for R2
First, simplify the equation:

\[ 2880 = \frac{24000R2}{100} \]

Multiply both sides by 100:

\[ 288000 = 24000R2 \]

Now, divide both sides by 24000 to find R2:

\[ R2 = \frac{288000}{24000} = 12 \]

### Conclusion
The rate of interest (R2) at which the same amount of simple interest can be received in 6 years is **12%**.