The rate of interest for the first 2 years is 3% per annum, for the next 3 years is 8% per annum and for the period beyond 5 years 10% per annum, If a man gets Rs. 1520 as a simple interest for 6 years, how much money did he deposit?

Options

A. Rs. 2500
B. Rs. 2800
C. Rs. 3500
D. Rs. 3800

Answer

To find out how much money the man deposited, we can use the formula for Simple Interest (SI):

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

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the initial amount deposited)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

Given:
- Total Simple Interest (SI) = Rs. 1520
- Time (T) = 6 years

### Step 1: Calculate the total interest rate over 6 years
The interest rates are given for different time periods:
- For the first 2 years: 3% per annum
- For the next 3 years: 8% per annum
- For the last 1 year (6th year): 10% per annum

Now, let's calculate the total interest rate for each period:
1. For the first 2 years at 3%:
\[ \text{Interest for 2 years} = 2 \times 3\% = 6\% \]

2. For the next 3 years at 8%:
\[ \text{Interest for 3 years} = 3 \times 8\% = 24\% \]

3. For the last year at 10%:
\[ \text{Interest for 1 year} = 10\% \]

Now, add these percentages together to find the total interest rate over 6 years:
\[ \text{Total Interest Rate} = 6\% + 24\% + 10\% = 40\% \]

### Step 2: Set up the equation for Simple Interest
Using the Simple Interest formula, we can express it as:
\[ 1520 = \frac{P \times 40 \times 6}{100} \]

### Step 3: Simplify the equation
Rearranging the equation gives:
\[ 1520 = \frac{240P}{100} \]
\[ 1520 = 2.4P \]

### Step 4: Solve for P (Principal)
To find \( P \), divide both sides by 2.4:
\[ P = \frac{1520}{2.4} \]
\[ P = 633.33 \]

### Step 5: Calculate the Principal
Now, we can calculate the principal amount:
\[ P = 633.33 \]

### Step 6: Check the options
The options provided are:
1. 2500
2. 2800
3. 3500
4. 3800

None of these options match our calculation. Let's check the calculations again.

### Correct Calculation
Let's re-evaluate the calculations for the principal amount.

Using the total interest rate of 40% for 6 years:
\[ 1520 = \frac{P \times 40}{100} \]
\[ 1520 = 0.4P \]
\[ P = \frac{1520}{0.4} \]
\[ P = 3800 \]

### Final Answer
The principal amount deposited is Rs. 3800.