An interest of Rs 8384 is received when a certain sum is invested for 4 years in scheme A which offers simple interest at `8%` per annum. When the same sum of money is invested for 6 years in scheme B which also offers simple interest at a certain rate, the amount received is Rs 39562, what is the rate of interest offered by scheme B ?

Options

A. 8.5
B. 7.25
C. 7.5
D. 8.25

Answer

To solve the problem step by step, we will use the formula for simple interest and the information provided in the question.

### Step 1: Understand the Simple Interest Formula
The formula for calculating simple interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the initial sum of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Calculate the Principal Amount from Scheme A
From the question, we know that the interest received from Scheme A is Rs 8384, the rate is 8% per annum, and the time is 4 years. We can plug these values into the formula to find the principal \( P \).

Using the formula:
\[ 8384 = \frac{P \times 8 \times 4}{100} \]

### Step 3: Rearranging the Equation
Rearranging the equation to solve for \( P \):
\[ P = \frac{8384 \times 100}{8 \times 4} \]
\[ P = \frac{838400}{32} \]
\[ P = 26200 \]

### Step 4: Calculate the Interest for Scheme B
Now that we have the principal amount \( P = 26200 \), we can find the interest earned when this amount is invested in Scheme B for 6 years, where the total amount received is Rs 39562.

First, we calculate the interest \( SI_B \) in Scheme B:
\[ SI_B = \text{Total Amount} - \text{Principal} \]
\[ SI_B = 39562 - 26200 = 13362 \]

### Step 5: Use the Simple Interest Formula for Scheme B
Now we can use the simple interest formula again to find the rate \( R \) for Scheme B:
\[ 13362 = \frac{26200 \times R \times 6}{100} \]

### Step 6: Rearranging to Solve for \( R \)
Rearranging the equation to isolate \( R \):
\[ R = \frac{13362 \times 100}{26200 \times 6} \]
\[ R = \frac{1336200}{157200} \]
\[ R = 8.5 \]

### Conclusion
The rate of interest offered by Scheme B is **8.5%**.

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