A sum of money invested at 9% per annum simple interest amounts to Rs. 37760 in 2 years. What will it amount to in 3 years at 10% per annum?

Answer

To solve the problem step by step, we will first determine the principal amount using the information given about the simple interest at 9% per annum for 2 years, and then we will calculate the amount for 3 years at 10% per annum.

### Step 1: Calculate the Simple Interest for 2 Years
We know that:
- Amount (A) = Rs. 37,760
- Rate (R) = 9% per annum
- Time (T) = 2 years

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

### Step 2: Substitute the values into the formula
We can express the amount in terms of principal (P):
\[ 37760 = P + \frac{P \times 9 \times 2}{100} \]

### Step 3: Simplify the equation
This simplifies to:
\[ 37760 = P + \frac{18P}{100} \]
\[ 37760 = P + 0.18P \]
\[ 37760 = 1.18P \]

### Step 4: Solve for Principal (P)
Now, we can solve for P:
\[ P = \frac{37760}{1.18} \]
\[ P = 32000 \]

### Step 5: Calculate Simple Interest for 3 Years at 10%
Now that we have the principal amount, we will calculate the amount for 3 years at 10% per annum:
- New Rate (R) = 10%
- New Time (T) = 3 years

Using the simple interest formula:
\[ SI = \frac{P \times R \times T}{100} \]
\[ SI = \frac{32000 \times 10 \times 3}{100} \]
\[ SI = \frac{320000}{100} \]
\[ SI = 3200 \]

### Step 6: Calculate the Total Amount for 3 Years
Now, we can find the total amount:
\[ A = P + SI \]
\[ A = 32000 + 3200 \]
\[ A = 35200 \]

### Final Answer
The amount after 3 years at 10% per annum will be Rs. 35,200.

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