Rs. 4,300 becomes Rs. 4,644 in 2 years at simple interest. Find the principle amount that will become ' Rs. 10,104 in 5 years at the same rate of interest

Options

A. Rs 5,710
B. Rs 8420
C. Rs 9,260
D. Rs 7,20

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the Simple Interest
We know that the principal amount (P) is Rs. 4,300, the amount (A) after 2 years is Rs. 4,644, and the time (T) is 2 years. We can find the simple interest (SI) using the formula:

\[ SI = A - P \]

Substituting the values:

\[ SI = 4644 - 4300 = 344 \]

### Step 2: Calculate the Rate of Interest
Using the simple interest formula:

\[ SI = \frac{P \times R \times T}{100} \]

We can rearrange this to find the rate (R):

\[ R = \frac{SI \times 100}{P \times T} \]

Substituting the known values:

\[ R = \frac{344 \times 100}{4300 \times 2} \]

Calculating this gives:

\[ R = \frac{34400}{8600} = 4\% \]

### Step 3: Set Up the Equation for the New Principal
Now we need to find the principal amount (let's call it \( x \)) that will become Rs. 10,104 in 5 years at the same rate of interest (4%).

Using the formula for the amount:

\[ A = P + SI \]

Where:

\[ SI = \frac{x \times R \times T}{100} \]

So we can write:

\[ 10104 = x + \frac{x \times 4 \times 5}{100} \]

### Step 4: Simplify the Equation
Substituting the rate and time into the equation:

\[ 10104 = x + \frac{20x}{100} \]

This simplifies to:

\[ 10104 = x + 0.2x \]

Combining like terms:

\[ 10104 = 1.2x \]

### Step 5: Solve for \( x \)
Now we can solve for \( x \):

\[ x = \frac{10104}{1.2} \]

Calculating this gives:

\[ x = 8420 \]

### Conclusion
The principal amount that will become Rs. 10,104 in 5 years at the same rate of interest is Rs. 8,420.

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