5000 becomes 5750 in 4 Years at certain rate of interest. If the rate of inerest had been 2% less then find the amount ?

Options

A. Rs 5250
B. Rs 5400
C. Rs 5350
D. Rs 5300

Answer

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

### Step 1: Identify the given values
- Principal (P) = 5000
- Amount (A) = 5750
- Time (T) = 4 years

### Step 2: Calculate the Simple Interest (SI)
Simple Interest can be calculated using the formula:
\[ \text{SI} = \text{A} - \text{P} \]

Substituting the values:
\[ \text{SI} = 5750 - 5000 = 750 \]

### Step 3: Use the Simple Interest formula to find the rate of interest (R)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Rearranging to find R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

Substituting the known values:
\[ R = \frac{750 \times 100}{5000 \times 4} \]

Calculating:
\[ R = \frac{75000}{20000} = 3.75\% \]

### Step 4: Determine the new rate of interest
If the rate of interest had been 2% less:
\[ \text{New Rate} = R - 2 = 3.75 - 2 = 1.75\% \]

### Step 5: Calculate the new Simple Interest with the new rate
Using the same Simple Interest formula:
\[ \text{New SI} = \frac{P \times \text{New Rate} \times T}{100} \]

Substituting the values:
\[ \text{New SI} = \frac{5000 \times 1.75 \times 4}{100} \]

Calculating:
\[ \text{New SI} = \frac{35000}{100} = 350 \]

### Step 6: Calculate the new amount
The new amount can be calculated as:
\[ \text{New Amount} = \text{Principal} + \text{New SI} \]
\[ \text{New Amount} = 5000 + 350 = 5350 \]

### Final Answer
The new amount after applying the reduced rate of interest is **5350**.

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