Rs 6,000 becomes Rs. 7,200 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be

Options

A. Rs 8,000
B. Rs 8,250
C. Rs 9,250
D. Rs 9,000

Answer

To solve the problem step by step, we will calculate the simple interest and the amount for the given principal, rate, and time.

### Step 1: Identify the given values
- Principal (P) = Rs 6,000
- Amount (A) after 4 years = Rs 7,200
- Time (T) = 4 years

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = A - P \]

Substituting the values:
\[ \text{SI} = 7,200 - 6,000 = 1,200 \]

### Step 3: Calculate the Rate of Interest (R)
To find the rate of interest, we can use the formula:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

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

Substituting the known values:
\[ R = \frac{1,200 \times 100}{6,000 \times 4} \]

Calculating:
\[ R = \frac{120,000}{24,000} = 5\% \]

### Step 4: Calculate the new rate of interest
If the rate becomes 1.5 times of itself:
\[ \text{New Rate} = 1.5 \times R = 1.5 \times 5\% = 7.5\% \]

### Step 5: Calculate the Simple Interest for the new rate over 5 years
Using the same formula for Simple Interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Substituting the new rate and time:
\[ \text{SI} = \frac{6,000 \times 7.5 \times 5}{100} \]

Calculating:
\[ \text{SI} = \frac{6,000 \times 7.5 \times 5}{100} = \frac{225,000}{100} = 2,250 \]

### Step 6: Calculate the total amount after 5 years
The total amount (A) is given by:
\[ A = P + \text{SI} \]

Substituting the values:
\[ A = 6,000 + 2,250 = 8,250 \]

### Final Answer
The amount of the same principal in 5 years at the new rate of interest is Rs 8,250.

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