A sum invested at 5% simple interest per annum increase to Rs. 504 in 4 years. The same amount at 10% simple interest per annum in `2(1)/(2)` years will grow to-:

Options

A. Rs. 420
B. Rs. 450
C. Rs. 525
D. Rs. 550

Answer

To solve the problem step by step, we will first find the principal amount using the information given about the investment at 5% simple interest, and then we will calculate the amount when the same principal is invested at 10% simple interest for 2.5 years.

### Step 1: Calculate the Principal Amount
We know that the amount (A) after 4 years at 5% simple interest is Rs. 504. The formula for simple interest is:

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

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of Interest
- \( T \) = Time in years

The total amount after 4 years is given by:

\[ A = P + SI \]

Substituting the values we have:

\[ 504 = P + \frac{P \times 5 \times 4}{100} \]

### Step 2: Simplify the Equation
We can rewrite the equation as:

\[ 504 = P + \frac{20P}{100} \]

This simplifies to:

\[ 504 = P + \frac{P}{5} \]

Combining the terms on the right side:

\[ 504 = \frac{5P + P}{5} = \frac{6P}{5} \]

### Step 3: Solve for Principal (P)
To find \( P \), we multiply both sides by 5:

\[ 504 \times 5 = 6P \]

Calculating the left side:

\[ 2520 = 6P \]

Now, divide both sides by 6:

\[ P = \frac{2520}{6} = 420 \]

### Step 4: Calculate Simple Interest at 10%
Now that we have the principal amount \( P = 420 \), we need to calculate the amount after investing this principal at 10% for 2.5 years.

Using the simple interest formula again:

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

Substituting \( P = 420 \), \( R = 10 \), and \( T = 2.5 \):

\[ SI = \frac{420 \times 10 \times 2.5}{100} \]

### Step 5: Simplify and Calculate SI
Calculating the SI:

\[ SI = \frac{420 \times 25}{100} = \frac{10500}{100} = 105 \]

### Step 6: Calculate Total Amount
Now we can find the total amount after 2.5 years:

\[ A = P + SI = 420 + 105 = 525 \]

### Final Answer
The amount after 2.5 years at 10% simple interest will grow to Rs. 525.

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