A sum of Rs. 6,000 amounts to 7,800 in 4 years at simple interset. If the interset rate is increased by 2.5%, then the same sum in same time would amount to:

Options

A. Rs 8,600
B. Rs, 9,200
C. Rs. 8,400
D. Rs. 8,500

Answer

To solve the problem step-by-step, we will follow the logical flow as discussed in the video transcript.

### Step 1: Identify the given values
- Principal (P) = Rs. 6000
- Amount (A) = Rs. 7800
- Time (T) = 4 years

### Step 2: Calculate the Simple Interest (SI)
The formula for the amount in terms of principal and simple interest is:
\[ A = P + SI \]
Rearranging gives:
\[ SI = A - P \]
Substituting the known values:
\[ SI = 7800 - 6000 = 1800 \]

### Step 3: Use the Simple Interest formula to find the rate (R)
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 1800 = \frac{6000 \times R \times 4}{100} \]
To simplify, we can multiply both sides by 100:
\[ 180000 = 6000 \times R \times 4 \]
Now, divide both sides by \( 6000 \times 4 \):
\[ R = \frac{180000}{24000} = 7.5\% \]

### Step 4: Increase the rate by 2.5%
New rate \( R' = 7.5\% + 2.5\% = 10\% \)

### Step 5: Calculate the new Simple Interest with the increased rate
Using the simple interest formula again:
\[ SI' = \frac{P \times R' \times T}{100} \]
Substituting the new rate:
\[ SI' = \frac{6000 \times 10 \times 4}{100} \]
Calculating:
\[ SI' = \frac{240000}{100} = 2400 \]

### Step 6: Calculate the new amount
Using the amount formula:
\[ A' = P + SI' \]
Substituting the values:
\[ A' = 6000 + 2400 = 8400 \]

### Final Answer
The new amount after increasing the interest rate by 2.5% is Rs. 8400.

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