The simple interset accured on a sum of Rs. 15000 at the end of 5 years is Rs. 9, 750 . If the rate of interset is 3% lesser, then the interset would be

Options

A. Rs. 7950
B. Rs. 5850
C. Rs. 3250
D. Rs. 7500

Answer

To solve the problem step by step, we will first determine the original rate of interest and then calculate the new interest when the rate is reduced by 3%.

### Step 1: Identify the given values
- Principal (P) = Rs 15,000
- Time (T) = 5 years
- Simple Interest (SI) = Rs 9,750

### Step 2: Use the formula for Simple Interest
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of Interest
- T = Time in years

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 9,750 = \frac{15,000 \times R \times 5}{100} \]

### Step 4: Rearrange the equation to solve for R
To isolate R, we can rearrange the equation:
\[ 9,750 \times 100 = 15,000 \times R \times 5 \]
\[ 975,000 = 75,000R \]
\[ R = \frac{975,000}{75,000} \]
\[ R = 13\% \]

### Step 5: Calculate the new rate of interest
Since the new rate is 3% lesser than the original rate:
\[ New\ Rate = 13\% - 3\% = 10\% \]

### Step 6: Calculate the new Simple Interest with the reduced rate
Using the new rate (10%) in the Simple Interest formula:
\[ SI_{new} = \frac{P \times R_{new} \times T}{100} \]
Substituting the values:
\[ SI_{new} = \frac{15,000 \times 10 \times 5}{100} \]
\[ SI_{new} = \frac{750,000}{100} \]
\[ SI_{new} = 7,500 \]

### Conclusion
The new Simple Interest when the rate is reduced by 3% is Rs 7,500.

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