The simple interest on an amount of Rs. 2800 at the end of 3 years is Rs. 420. What would be the simple interest on an amount of Rs. 3200 for the same rate and the same period ?

Options

A. Rs. 560
B. Rs. 640
C. Rs. 480
D. Rs. 440

Answer

To solve the problem step by step, we will first find the rate of interest using the given information and then calculate the simple interest for the new principal amount.

### Step 1: Identify the given information
- Principal (P1) = Rs. 2800
- Simple Interest (SI1) = Rs. 420
- Time (T) = 3 years

### Step 2: Use the formula for Simple Interest
The formula for 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: Rearrange the formula to find the rate (R)
From the formula, we can rearrange it to find the rate:
\[ R = \frac{SI \times 100}{P \times T} \]

### Step 4: Substitute the known values to find R
Substituting the values we have:
\[ R = \frac{420 \times 100}{2800 \times 3} \]
Calculating the denominator:
\[ 2800 \times 3 = 8400 \]
Now substituting this back into the equation:
\[ R = \frac{42000}{8400} \]
Calculating:
\[ R = 5\% \]

### Step 5: Calculate the Simple Interest for the new principal
Now, we need to calculate the simple interest for the new principal amount (P2 = Rs. 3200) using the same rate and time:
- Principal (P2) = Rs. 3200
- Rate (R) = 5%
- Time (T) = 3 years

Using the simple interest formula again:
\[ SI2 = \frac{P2 \times R \times T}{100} \]

### Step 6: Substitute the known values to find SI2
Substituting the values:
\[ SI2 = \frac{3200 \times 5 \times 3}{100} \]
Calculating:
\[ SI2 = \frac{48000}{100} = 480 \]

### Final Answer
The simple interest on an amount of Rs. 3200 for the same rate and the same period is Rs. 480.

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