Simple Interest Calculation:

To calculate the simple interest, we need to know the principal amount, rate of interest, and the time period.

Given:
Principal amount (P) = Rs 8000
Simple Interest (SI) = Rs 6875
Rate of Interest (R) = ?
Time period (T) = ?

Step 1: Calculating the Rate of Interest (R)

We can use the formula for simple interest to calculate the rate of interest:

SI = (P * R * T) / 100

Substituting the given values:

6875 = (8000 * R * T) / 100

Step 2: Calculating the Time Period (T)

To calculate the time period, we need to rearrange the formula:

T = (SI * 100) / (P * R)

Substituting the given values:

T = (6875 * 100) / (8000 * R)

Step 3: Calculating the Rate of Interest (R) and Time Period (T)

As we have two unknowns, R and T, we need another equation to solve for both variables. One possible equation is the given condition that Rs 8000 becomes Rs 10000.

Using the formula for simple interest, we can write:

10000 = 8000 + SI

10000 = 8000 + (8000 * R * T) / 100

Simplifying the equation:

2000 = (8000 * R * T) / 100

Rearranging the equation:

R * T = (2000 * 100) / 8000

R * T = 25

Now, we can substitute the value of T from step 2 into this equation:

R * [(6875 * 100) / (8000 * R)] = 25

Simplifying the equation:

R * 6875 = 2000

R = 2000 / 6875

R ≈ 0.29

Step 4: Calculating the Time Period (T)

Substituting the value of R into the equation from step 2:

T = (6875 * 100) / (8000 * 0.29)

T ≈ 30

Therefore, the rate of interest is approximately 0.29 (or 29%) and the time period is approximately 30 years.