A sum of money is to be divided among A, B and C in the ratio 2: 3: 7. If the total share of A and B together is Rs. 1500 less than C. What is A's share in it?

Options

A. Rs 1000
B. Rs 1500
C. Rs 2000
D. data inadequate

Answer

To solve the problem of dividing a sum of money among A, B, and C in the ratio 2:3:7, we can follow these steps:

### Step 1: Define the Ratio
Let the shares of A, B, and C be represented as:
- A's share = 2x
- B's share = 3x
- C's share = 7x

### Step 2: Express the Total Share of A and B
The total share of A and B together can be calculated as:
\[ \text{Total share of A and B} = A's \, share + B's \, share = 2x + 3x = 5x \]

### Step 3: Set Up the Equation
According to the problem, the total share of A and B together is Rs. 1500 less than C's share. Therefore, we can set up the equation:
\[ 5x = 7x - 1500 \]

### Step 4: Solve the Equation
Now, we can solve for x:
1. Rearranging the equation gives:
\[ 5x + 1500 = 7x \]
2. Subtracting 5x from both sides results in:
\[ 1500 = 7x - 5x \]
\[ 1500 = 2x \]
3. Dividing both sides by 2 gives:
\[ x = 750 \]

### Step 5: Calculate A's Share
Now that we have the value of x, we can find A's share:
\[ A's \, share = 2x = 2 \times 750 = 1500 \]

### Conclusion
Thus, A's share in the money is Rs. 1500.

---