Rs . 6000 becomes Rs, 7200 in 4 years. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be

Answer

To solve the problem step by step, we will first determine the rate of interest and then calculate the amount after 5 years when the rate becomes 1.5 times the original rate.

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

### Step 2: Calculate the Simple Interest (SI)
We know that:
\[ \text{SI} = \text{Amount} - \text{Principal} \]
So,
\[ \text{SI} = 7200 - 6000 = 1200 \]

### Step 3: Use the Simple Interest formula to find the rate (R)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 1200 = \frac{6000 \times R \times 4}{100} \]

### Step 4: Simplify the equation
Multiply both sides by 100 to eliminate the fraction:
\[ 1200 \times 100 = 6000 \times R \times 4 \]
\[ 120000 = 24000R \]

### Step 5: Solve for R
Now divide both sides by 24000:
\[ R = \frac{120000}{24000} = 5\% \]

### Step 6: Calculate the new rate (R')
The new rate is 1.5 times the original rate:
\[ R' = 1.5 \times R = 1.5 \times 5\% = 7.5\% \]

### Step 7: Calculate the amount after 5 years using the new rate
Now we will find the amount (A') after 5 years using the new rate:
\[ A' = P + \text{SI'} \]
Where:
\[ \text{SI'} = \frac{P \times R' \times T'}{100} \]
Here, \( T' = 5 \) years.

Substituting the values:
\[ \text{SI'} = \frac{6000 \times 7.5 \times 5}{100} \]

### Step 8: Simplify to find SI'
Calculating:
\[ \text{SI'} = \frac{6000 \times 7.5 \times 5}{100} = \frac{6000 \times 37.5}{100} = \frac{225000}{100} = 2250 \]

### Step 9: Calculate the final amount A'
Now substitute SI' back into the amount formula:
\[ A' = 6000 + 2250 = 8250 \]

### Final Answer
The amount after 5 years when the rate becomes 1.5 times of itself is Rs. 8250.

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