What amount of money is divided between A, B and C. If B and C together get Rs. 100 and A gets twice as much as B while C with A gets Rs. 150 ?

Answer

To solve the problem step by step, let's denote the amounts received by A, B, and C as follows:

- Let the amount received by B be \( b \).
- Since A gets twice as much as B, the amount received by A will be \( a = 2b \).
- The amount received by C will be denoted as \( c \).

### Step 1: Set up the equations based on the information given.

From the problem, we know:
1. B and C together get Rs. 100:
\[ b + c = 100 \quad \text{(Equation 1)} \]

2. C and A together get Rs. 150:
\[ c + a = 150 \quad \text{(Equation 2)} \]

### Step 2: Substitute A in terms of B into Equation 2.

Since \( a = 2b \), we can substitute this into Equation 2:
\[ c + 2b = 150 \quad \text{(Equation 3)} \]

### Step 3: Solve the equations.

Now we have two equations:
1. \( b + c = 100 \) (Equation 1)
2. \( c + 2b = 150 \) (Equation 3)

Let's subtract Equation 1 from Equation 3:
\[ (c + 2b) - (b + c) = 150 - 100 \]
This simplifies to:
\[ 2b - b = 50 \]
\[ b = 50 \]

### Step 4: Find the value of A.

Now that we have \( b \), we can find \( a \):
\[ a = 2b = 2 \times 50 = 100 \]

### Step 5: Find the value of C.

Now we can substitute \( b \) back into Equation 1 to find \( c \):
\[ b + c = 100 \]
\[ 50 + c = 100 \]
\[ c = 100 - 50 = 50 \]

### Step 6: Calculate the total amount.

Now we have:
- \( a = 100 \)
- \( b = 50 \)
- \( c = 50 \)

The total amount of money divided among A, B, and C is:
\[ a + b + c = 100 + 50 + 50 = 200 \]

### Final Answer:
The total amount of money divided between A, B, and C is Rs. 200.

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