The rate of interest for the first 2 years is` 5%` for the next 3 years is` 8%` and beyond this. It is` 10%` per annum. If the simple interest for 8 years is Rs. 1280. What is the principal ?

Options

A. Rs. 2500
B. Rs. 2000
C. Rs. 3200
D. Rs. 2440

Answer

To find the principal amount based on the given rates of interest and the total simple interest earned over 8 years, we can follow these steps:

### Step 1: Identify the rates and time periods
- For the first 2 years, the rate of interest (R1) is 5%.
- For the next 3 years (years 3 to 5), the rate of interest (R2) is 8%.
- For the remaining 3 years (years 6 to 8), the rate of interest (R3) is 10%.

### Step 2: Calculate the total interest for each period
- **Interest for the first 2 years (I1)**:
\[ I_1 = P \times \frac{R_1}{100} \times T_1 = P \times \frac{5}{100} \times 2 = \frac{10P}{100} = 0.1P \]

- **Interest for the next 3 years (I2)**:
\[ I_2 = P \times \frac{R_2}{100} \times T_2 = P \times \frac{8}{100} \times 3 = \frac{24P}{100} = 0.24P \]

- **Interest for the last 3 years (I3)**:
\[ I_3 = P \times \frac{R_3}{100} \times T_3 = P \times \frac{10}{100} \times 3 = \frac{30P}{100} = 0.3P \]

### Step 3: Calculate the total simple interest
The total simple interest (SI) for 8 years is the sum of the interests from all three periods:
\[ SI = I_1 + I_2 + I_3 = 0.1P + 0.24P + 0.3P = 0.64P \]

### Step 4: Set up the equation with the given total interest
We know that the total simple interest for 8 years is Rs. 1280. Therefore, we can set up the equation:
\[ 0.64P = 1280 \]

### Step 5: Solve for the principal (P)
To find the principal, we divide both sides by 0.64:
\[ P = \frac{1280}{0.64} = 2000 \]

### Conclusion
The principal amount is Rs. 2000.

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