Rashmi lent X 600 to Geeta for 2 yr and ? 150 to Seeta for 4 yr and received altogether X 80 as simple interest from both. Find the rate of interest.

Options

A. `3(4)/(9)`
B. `2(4)/(9)`
C. `5(4)/(9)`
D. `4(4)/(9)`

Answer

To solve the problem step by step, we will follow the process of calculating the simple interest for both Geeta and Seeta, and then find the rate of interest.

### Step 1: Calculate the Simple Interest for Geeta
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount
- \(R\) = Rate of interest
- \(T\) = Time in years

For Geeta:
- Principal \(P = 600\)
- Time \(T = 2\) years

So, the Simple Interest for Geeta is:
\[ SI_{Geeta} = \frac{600 \times R \times 2}{100} = \frac{1200R}{100} = 12R \]

### Step 2: Calculate the Simple Interest for Seeta
For Seeta:
- Principal \(P = 150\)
- Time \(T = 4\) years

So, the Simple Interest for Seeta is:
\[ SI_{Seeta} = \frac{150 \times R \times 4}{100} = \frac{600R}{100} = 6R \]

### Step 3: Calculate the Total Simple Interest
According to the problem, the total Simple Interest received from both Geeta and Seeta is \(80\):
\[ SI_{Total} = SI_{Geeta} + SI_{Seeta} = 12R + 6R = 18R \]
Setting this equal to the total interest received:
\[ 18R = 80 \]

### Step 4: Solve for the Rate of Interest \(R\)
To find \(R\), we can rearrange the equation:
\[ R = \frac{80}{18} = \frac{40}{9} \]

### Step 5: Convert to Percentage
To express \(R\) as a percentage:
\[ R = \frac{40}{9} \approx 4.44\% \]

### Final Answer
The rate of interest is approximately \(4 \frac{4}{9}\%\).

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