A sum invested at the rate of interest 5% S.I grows to Rs. 5400 in 4 years. The same amount in 3 years at the rate of 10% per annum S.I will grow to

Options

A. Rs. 5700
B. Rs. 5750
C. Rs. 5800
D. Rs. 5850

Answer

To solve the problem step by step, we need to first determine the principal amount (P) that grows to Rs. 5400 at a 5% simple interest rate over 4 years. Then, we will calculate how much this principal amount will grow in 3 years at a 10% interest rate.

### Step 1: Find the Principal Amount (P)

We know that the formula for the total amount (A) in simple interest is given by:

\[ A = P + SI \]

Where:
- \( SI = \frac{P \times R \times T}{100} \)
- \( A \) is the total amount after time \( T \)
- \( P \) is the principal amount
- \( R \) is the rate of interest
- \( T \) is the time in years

Given:
- \( A = 5400 \)
- \( R = 5\% \)
- \( T = 4 \)

We can substitute the values into the formula for simple interest:

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

This simplifies to:

\[ SI = \frac{20P}{100} = \frac{P}{5} \]

Now substituting \( SI \) back into the total amount formula:

\[ 5400 = P + \frac{P}{5} \]

To combine the terms on the right side, we can express \( P \) as a fraction:

\[ 5400 = P + 0.2P = 1.2P \]

Now, we can solve for \( P \):

\[ P = \frac{5400}{1.2} \]

Calculating this gives:

\[ P = 4500 \]

### Step 2: Calculate the Amount in 3 Years at 10% Interest

Now that we have the principal amount \( P = 4500 \), we need to calculate how much this amount will grow in 3 years at a 10% interest rate.

Using the same formula for total amount:

\[ A = P + SI \]

Where:

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

Given:
- \( R = 10\% \)
- \( T = 3 \)

Substituting the values:

\[ SI = \frac{4500 \times 10 \times 3}{100} \]

This simplifies to:

\[ SI = \frac{45000}{100} = 450 \]

Now substituting \( SI \) back into the total amount formula:

\[ A = 4500 + 450 = 4950 \]

### Final Answer

The amount after 3 years at 10% interest will be Rs. 4950.

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