Nikhil invested certain amount in three different schemes A,B and C with the rate of interest 10% per annum, 12% per annum and 15% per annum, respectively., if the toal interest in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B,what was the amount invested in scheme B? ?

Answer

To solve the problem step by step, we will define the amounts invested in each scheme and set up equations based on the information provided.

### Step 1: Define the Variables
Let:
- Amount invested in Scheme A = \( A \)
- Amount invested in Scheme B = \( B \)
- Amount invested in Scheme C = \( C \)

### Step 2: Set Up Relationships
From the problem, we know:
1. The interest rates are:
- Scheme A: 10% per annum
- Scheme B: 12% per annum
- Scheme C: 15% per annum

2. The total interest earned in one year is Rs. 3200.

3. The amount invested in Scheme C is:
- 150% of the amount invested in Scheme A:
\[ C = 1.5A \]
- 240% of the amount invested in Scheme B:
\[ C = 2.4B \]

### Step 3: Express C in Terms of A and B
From the equations for C, we can express A and B in terms of C:
1. From \( C = 1.5A \):
\[ A = \frac{C}{1.5} = \frac{2C}{3} \]

2. From \( C = 2.4B \):
\[ B = \frac{C}{2.4} = \frac{5C}{12} \]

### Step 4: Substitute into the Total Interest Equation
The total interest from all three schemes can be expressed as:
\[ \text{Total Interest} = \left( \frac{10}{100} A \right) + \left( \frac{12}{100} B \right) + \left( \frac{15}{100} C \right) = 3200 \]

Substituting \( A \) and \( B \) in terms of \( C \):
\[ \frac{10}{100} \left( \frac{2C}{3} \right) + \frac{12}{100} \left( \frac{5C}{12} \right) + \frac{15}{100} C = 3200 \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ \frac{10C}{300} + \frac{60C}{1200} + \frac{15C}{100} = 3200 \]

Converting all terms to a common denominator (300):
\[ \frac{10C}{300} + \frac{15C}{300} + \frac{45C}{300} = 3200 \]
\[ \frac{70C}{300} = 3200 \]

### Step 6: Solve for C
Multiply both sides by 300:
\[ 70C = 3200 \times 300 \]
\[ 70C = 960000 \]
\[ C = \frac{960000}{70} = 13714.29 \text{ (approximately)} \]

### Step 7: Find the Amounts for A and B
Now, substitute \( C \) back to find \( A \) and \( B \):
1. For \( A \):
\[ A = \frac{2C}{3} = \frac{2 \times 13714.29}{3} \approx 9142.86 \]

2. For \( B \):
\[ B = \frac{5C}{12} = \frac{5 \times 13714.29}{12} \approx 5714.29 \]

### Final Answer
The amount invested in Scheme B is approximately Rs. 5714.29.

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