Mr.Thakur ji invested a total amount of `Rs.1,39,000` in two different schemes "Dhan Vridhi" and "Dhan Varsha" at the simple interest rate of `14% p.a.` and `11% p.a.` respectively. If the total amount of simple interest earned in `2` years be `Rs.35,080`, what was the amount invested in Scheme Dhan Varsha?

Options

A. Rs.6400
B. Rs.7200
C. Rs.6500
D. Rs.7500

Answer

To solve the problem step by step, we need to determine how much Mr. Thakur ji invested in the "Dhan Varsha" scheme. Let's break it down:

### Step 1: Define Variables
Let:
- \( X \) = Amount invested in "Dhan Varsha"
- \( 139000 - X \) = Amount invested in "Dhan Vridhi"

### Step 2: Write Down the Simple Interest Formula
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 3: Calculate Simple Interest for Each Scheme
For "Dhan Varsha" (11% per annum for 2 years):
\[ SI_{Dhan Varsha} = \frac{X \times 11 \times 2}{100} = \frac{22X}{100} = 0.22X \]

For "Dhan Vridhi" (14% per annum for 2 years):
\[ SI_{Dhan Vridhi} = \frac{(139000 - X) \times 14 \times 2}{100} = \frac{28(139000 - X)}{100} = 0.28(139000 - X) \]

### Step 4: Set Up the Equation
According to the problem, the total simple interest earned from both schemes in 2 years is Rs. 35,080. Therefore, we can write:
\[ 0.22X + 0.28(139000 - X) = 35080 \]

### Step 5: Simplify the Equation
Expanding the equation:
\[ 0.22X + 0.28 \times 139000 - 0.28X = 35080 \]
Calculating \( 0.28 \times 139000 \):
\[ 0.28 \times 139000 = 38920 \]
So, the equation becomes:
\[ 0.22X + 38920 - 0.28X = 35080 \]

### Step 6: Combine Like Terms
Combining the \( X \) terms:
\[ (0.22 - 0.28)X + 38920 = 35080 \]
This simplifies to:
\[ -0.06X + 38920 = 35080 \]

### Step 7: Isolate \( X \)
Subtract 38920 from both sides:
\[ -0.06X = 35080 - 38920 \]
Calculating the right side:
\[ 35080 - 38920 = -3820 \]
Thus, we have:
\[ -0.06X = -3820 \]

### Step 8: Solve for \( X \)
Dividing both sides by -0.06:
\[ X = \frac{-3820}{-0.06} = 63666.67 \]
Since we need to round to the nearest whole number, we have:
\[ X \approx 63667 \]

### Step 9: Calculate the Amount Invested in Dhan Varsha
Thus, the amount invested in "Dhan Varsha" is approximately Rs. 63,667.