6000 becomes 7200in 4 Years at certain rate of interest. If the rate of interest becomes 1.5 times then find the amount?

Options

A. Rs 7800
B. Rs 8600
C. Rs 8400
D. Rs 8500

Answer

To solve the problem step by step, let's break it down:

### Step 1: Identify the given values
- Principal (P) = 6000
- Amount (A) = 7200
- Time (T) = 4 years

### Step 2: Calculate the Simple Interest (SI)
We can find the Simple Interest using the formula:
\[ SI = A - P \]
Substituting the values:
\[ SI = 7200 - 6000 = 1200 \]

### Step 3: Use the Simple Interest formula to find the rate of interest (R)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
We can rearrange this to find R:
\[ R = \frac{SI \times 100}{P \times T} \]
Substituting the known values:
\[ R = \frac{1200 \times 100}{6000 \times 4} \]
Calculating the right side:
\[ R = \frac{120000}{24000} = 5\% \]

### Step 4: Calculate the new rate of interest
The new rate of interest is 1.5 times the original rate:
\[ R_{new} = 5\% \times 1.5 = 7.5\% \]

### Step 5: Calculate the new Simple Interest (SI) with the new rate
Using the same formula for Simple Interest:
\[ SI_{new} = \frac{P \times R_{new} \times T}{100} \]
Substituting the values:
\[ SI_{new} = \frac{6000 \times 7.5 \times 4}{100} \]
Calculating:
\[ SI_{new} = \frac{180000}{100} = 1800 \]

### Step 6: Calculate the new amount (A)
The new amount can be calculated by adding the new Simple Interest to the principal:
\[ A_{new} = P + SI_{new} \]
Substituting the values:
\[ A_{new} = 6000 + 1800 = 7800 \]

### Final Answer
The new amount is **7800**.

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