A certain amount becomes Rs 2800 in 3 years and Rs 3000 in 5 years. Find the amount and rate of simple interest.

Options

A. `2000,5%`
B. `2400,5%`
C. `2500,4%`
D. `2500,3%`

Answer

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

### Step 1: Understand the given information
We know that:
- The amount becomes Rs 2800 in 3 years.
- The amount becomes Rs 3000 in 5 years.

### Step 2: Calculate the simple interest for the 2-year period
The simple interest earned from year 3 to year 5 can be calculated as follows:
- Amount after 5 years = Rs 3000
- Amount after 3 years = Rs 2800

The simple interest for the 2 years (from year 3 to year 5) is:
\[ \text{SI} = \text{Amount after 5 years} - \text{Amount after 3 years} = 3000 - 2800 = 200 \]

### Step 3: Calculate the simple interest per year
Since the interest earned over 2 years is Rs 200, the interest earned per year is:
\[ \text{SI per year} = \frac{200}{2} = 100 \]

### Step 4: Calculate the principal amount
Now, we can find the principal amount (P) using the information from the amount after 3 years:
\[ \text{Amount after 3 years} = \text{Principal} + \text{Simple Interest for 3 years} \]
The simple interest for 3 years is:
\[ \text{SI for 3 years} = 3 \times \text{SI per year} = 3 \times 100 = 300 \]
Thus, we can write:
\[ 2800 = P + 300 \]
Rearranging gives:
\[ P = 2800 - 300 = 2500 \]

### Step 5: Calculate the rate of interest
Now that we have the principal amount (P = Rs 2500), we can calculate the rate of interest (R) using the formula for simple interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest for 1 year = Rs 100
- P = Principal = Rs 2500
- T = Time = 1 year

Substituting the values:
\[ 100 = \frac{2500 \times R \times 1}{100} \]
Multiplying both sides by 100 gives:
\[ 10000 = 2500R \]
Now, solving for R:
\[ R = \frac{10000}{2500} = 4\% \]

### Final Answer
- Principal Amount (P) = Rs 2500
- Rate of Interest (R) = 4%

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