Aryan invested an sum of money at an annual simple interesst rate of 10%. At the end of four years the amount invested plus interest earned was Rs 770. The amount invested was:

Options

A. Rs 650
B. Rs 350
C. Rs 550
D. Rs 500

Answer

To find the amount invested by Aryan, we can follow these steps:

### Step 1: Understand the problem
We know that Aryan invested a sum of money at an annual simple interest rate of 10%. After 4 years, the total amount (principal + interest) is Rs 770.

### Step 2: Set up the formula for Simple Interest
The formula for calculating Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (the amount invested)
- \( R \) = Rate of interest (10%)
- \( T \) = Time (4 years)

### Step 3: Calculate the Interest earned
Using the formula, we can express the interest earned over 4 years:
\[ \text{SI} = \frac{P \times 10 \times 4}{100} \]
\[ \text{SI} = \frac{40P}{100} = \frac{2P}{5} \]

### Step 4: Write the equation for total amount
The total amount after 4 years is the sum of the principal and the interest earned:
\[ \text{Total Amount} = P + \text{SI} \]
Substituting the expression for SI:
\[ 770 = P + \frac{2P}{5} \]

### Step 5: Combine the terms
To combine the terms, we can express \( P \) as \( \frac{5P}{5} \):
\[ 770 = \frac{5P}{5} + \frac{2P}{5} \]
\[ 770 = \frac{5P + 2P}{5} \]
\[ 770 = \frac{7P}{5} \]

### Step 6: Solve for P
To isolate \( P \), multiply both sides by 5:
\[ 770 \times 5 = 7P \]
\[ 3850 = 7P \]
Now, divide both sides by 7:
\[ P = \frac{3850}{7} \]
\[ P = 550 \]

### Step 7: Conclusion
The amount invested by Aryan was Rs 550.

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