The compound interest on a certain sum of money at 5 % for 2 yr is Rs 328 . The simple interest on that sum at the same rate for the same period of time will be

Options

A. Rs 320
B. Rs 322
C. Rs 325
D. Rs 326

Answer

To solve the problem, we need to find the simple interest on a certain sum of money given that the compound interest for 2 years at a rate of 5% is Rs. 328.

### Step-by-step Solution:

1. **Understanding the Compound Interest**:
We know that the compound interest (CI) for 2 years is given as Rs. 328. The formula for compound interest can be expressed as:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where \(A\) is the total amount, \(P\) is the principal, \(r\) is the rate of interest, and \(n\) is the number of years.

2. **Finding the Amount**:
Since CI for 2 years is Rs. 328, we can express it as:
\[ CI = A - P \]
Rearranging gives:
\[ A = CI + P \]
We will need to find \(P\) first.

3. **Using the Successive Interest Rule**:
The rate of interest is 5%, which can be expressed as a fraction:
\[ \frac{5}{100} = \frac{1}{20} \]
If we assume the principal \(P\) is 400, we can calculate the amount after 2 years:
- After the first year:
\[ A_1 = P + \frac{5}{100} \times P = 400 + 20 = 420 \]
- After the second year:
\[ A_2 = A_1 + \frac{5}{100} \times A_1 = 420 + 21 = 441 \]

4. **Finding the Compound Interest**:
The compound interest from our assumed principal of Rs. 400 is:
\[ CI = A - P = 441 - 400 = 41 \]
We know from the problem that this CI corresponds to Rs. 328.

5. **Finding the Value of 1 Unit**:
We can set up a proportion:
\[ 41 \text{ units} = 328 \text{ Rs.} \]
Therefore, the value of 1 unit is:
\[ 1 \text{ unit} = \frac{328}{41} = 8 \text{ Rs.} \]

6. **Finding the Principal**:
Since we assumed \(P = 400\) units, we can find the actual principal:
\[ P = 400 \text{ units} \times 8 \text{ Rs/unit} = 3200 \text{ Rs.} \]

7. **Calculating Simple Interest**:
Now we can calculate the simple interest (SI) using the formula:
\[ SI = \frac{P \times r \times t}{100} \]
Substituting the values:
\[ SI = \frac{3200 \times 5 \times 2}{100} = \frac{32000}{100} = 320 \text{ Rs.} \]

### Final Answer:
The simple interest on that sum at the same rate for the same period of time will be **Rs. 320**.