If Rs. 500 amounts to the Rs. 725 at 9% simple interest in some time, what will Rs. 600 amount to at 11% in the same time?

Answer

To solve the problem step by step, we will first determine the time period using the information from the first case and then use that time to find the amount for the second case.

### Step 1: Identify the given values in the first case
- Principal (P) = Rs. 500
- Amount (A) = Rs. 725
- Rate of interest (R) = 9%

### Step 2: Use the formula for Simple Interest
The formula for the amount in terms of principal, interest, and time is:
\[ A = P + \text{SI} \]
Where Simple Interest (SI) is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

### Step 3: Substitute the values into the equation
Using the formula for the amount:
\[ 725 = 500 + \frac{500 \times 9 \times T}{100} \]

### Step 4: Rearrange the equation to find T
First, subtract 500 from both sides:
\[ 725 - 500 = \frac{500 \times 9 \times T}{100} \]
\[ 225 = \frac{500 \times 9 \times T}{100} \]

### Step 5: Simplify the equation
Multiply both sides by 100 to eliminate the fraction:
\[ 22500 = 500 \times 9 \times T \]
Now, simplify the right side:
\[ 22500 = 4500T \]

### Step 6: Solve for T
Divide both sides by 4500:
\[ T = \frac{22500}{4500} = 5 \text{ years} \]

### Step 7: Use the time found to calculate the amount in the second case
Now we will find the amount for the second case where:
- Principal (P') = Rs. 600
- Rate of interest (R') = 11%
- Time (T) = 5 years (from the first case)

### Step 8: Calculate the Simple Interest for the second case
Using the formula for Simple Interest:
\[ \text{SI'} = \frac{P' \times R' \times T}{100} \]
Substituting the values:
\[ \text{SI'} = \frac{600 \times 11 \times 5}{100} \]

### Step 9: Simplify the calculation
\[ \text{SI'} = \frac{33000}{100} = 330 \]

### Step 10: Calculate the total amount for the second case
Using the amount formula:
\[ A' = P' + \text{SI'} \]
Substituting the values:
\[ A' = 600 + 330 = 930 \]

### Final Answer
The amount that Rs. 600 will amount to at 11% in the same time is **Rs. 930**.

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