The sum of Rs 500 becomes Rs 600 in 2 years at certain rate of simple interest. If the rate of interset in halved, the what amount will Rs 500 given in 2 years ?

Options

A. A)Rs 520
B. B)Rs 560
C. C)Rs 550
D. D)Rs 500

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We know that a sum of Rs 500 becomes Rs 600 in 2 years at a certain rate of simple interest.

### Step 2: Calculate the interest earned
The interest earned over 2 years can be calculated as:
\[ \text{Interest} = \text{Final Amount} - \text{Principal} = 600 - 500 = Rs 100 \]

### Step 3: Find the rate of interest
Using the formula for simple interest:
\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount = Rs 500
- \( R \) = Rate of interest (unknown)
- \( T \) = Time in years = 2

We know that the interest earned in 2 years is Rs 100. So we can set up the equation:
\[ 100 = \frac{500 \times R \times 2}{100} \]

### Step 4: Solve for R
Rearranging the equation:
\[ 100 = \frac{1000R}{100} \]
\[ 100 = 10R \]
\[ R = \frac{100}{10} = 10\% \]

### Step 5: Halve the rate of interest
If the rate of interest is halved, the new rate \( R' \) will be:
\[ R' = \frac{10}{2} = 5\% \]

### Step 6: Calculate the new interest for 2 years at the new rate
Using the same formula for simple interest with the new rate:
\[ \text{SI'} = \frac{P \times R' \times T}{100} \]
Substituting the values:
\[ \text{SI'} = \frac{500 \times 5 \times 2}{100} \]
\[ \text{SI'} = \frac{5000}{100} = Rs 50 \]

### Step 7: Calculate the new final amount
Now, we find the new final amount after 2 years:
\[ \text{Final Amount} = \text{Principal} + \text{New Interest} = 500 + 50 = Rs 550 \]

### Conclusion
The amount that Rs 500 will become in 2 years at the halved rate of interest is Rs 550.