Sohail invested Rs. 5000 in a scheme offering 10% simple interest. If the same sum is invested in another scheme for 2 more years offering 15% simple interest then it would have fetched Rs. 2000 more. Find time period in years) of investment in first scheme.

Options

A. A)2.5
B. B)4
C. C)3
D. D)2

Answer

To solve the problem step-by-step, we will break it down into manageable parts:

### Step 1: Understand the Problem
Sohail invested Rs. 5000 in two different schemes. The first scheme offers 10% simple interest, and the second scheme offers 15% simple interest for 2 more years. The difference in interest earned from both schemes is Rs. 2000.

### Step 2: Define Variables
Let:
- \( t \) = time period (in years) of investment in the first scheme (10% interest).
- The time period for the second scheme will then be \( t + 2 \) years.

### Step 3: Calculate Interest for Both Schemes
Using the formula for simple interest:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and \( T \) is the time in years.

**Interest from the first scheme (10%):**
\[ I_1 = \frac{5000 \times 10 \times t}{100} = 500t \]

**Interest from the second scheme (15%):**
\[ I_2 = \frac{5000 \times 15 \times (t + 2)}{100} = 750(t + 2) \]

### Step 4: Set Up the Equation
According to the problem, the interest from the second scheme is Rs. 2000 more than the interest from the first scheme:
\[ I_2 - I_1 = 2000 \]
Substituting the expressions for \( I_1 \) and \( I_2 \):
\[ 750(t + 2) - 500t = 2000 \]

### Step 5: Simplify the Equation
Expanding the equation:
\[ 750t + 1500 - 500t = 2000 \]
Combine like terms:
\[ 250t + 1500 = 2000 \]

### Step 6: Solve for \( t \)
Subtract 1500 from both sides:
\[ 250t = 500 \]
Now, divide by 250:
\[ t = \frac{500}{250} = 2 \]

### Step 7: Conclusion
The time period of investment in the first scheme is \( t = 2 \) years.

### Final Answer
The time period of investment in the first scheme is **2 years**.

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