A sum of money put at 9% per annum simple interest amounts to Rs. 10160 in 3 years. What will it amount to in 2 years at 8% per annum?

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Given Information
We know that:
- The amount after 3 years at 9% per annum is Rs. 10,160.
- We need to find out how much this amount will be in 2 years at 8% per annum.

### Step 2: Find the Principal Amount
Let the principal amount be \( P \).

Using the formula for the amount in simple interest:
\[ A = P + SI \]
Where \( SI = \frac{P \times R \times T}{100} \)

Here, \( A = 10,160 \), \( R = 9\% \), and \( T = 3 \) years.

First, we calculate the simple interest:
\[ SI = \frac{P \times 9 \times 3}{100} = \frac{27P}{100} \]

Now, substituting \( SI \) into the amount formula:
\[ 10,160 = P + \frac{27P}{100} \]

### Step 3: Combine Like Terms
To combine the terms, we can express \( P \) as \( \frac{100P}{100} \):
\[ 10,160 = \frac{100P + 27P}{100} \]
\[ 10,160 = \frac{127P}{100} \]

### Step 4: Solve for Principal \( P \)
Now, we can solve for \( P \):
\[ 127P = 10,160 \times 100 \]
\[ 127P = 1,016,000 \]
\[ P = \frac{1,016,000}{127} \]
\[ P = 8,000 \]

### Step 5: Calculate Simple Interest for New Conditions
Now we have the principal amount \( P = 8,000 \). We need to find the amount after 2 years at 8% per annum.

Using the simple interest formula again:
\[ SI = \frac{P \times R \times T}{100} \]
Where \( R = 8\% \) and \( T = 2 \) years:
\[ SI = \frac{8,000 \times 8 \times 2}{100} \]
\[ SI = \frac{128,000}{100} = 1,280 \]

### Step 6: Calculate the Total Amount
Now, we can find the total amount after 2 years:
\[ A = P + SI \]
\[ A = 8,000 + 1,280 = 9,280 \]

### Final Answer
The amount after 2 years at 8% per annum will be Rs. 9,280.

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