We have to divide a sum of Rs. 13,950 among three persons A,B and C ,B must get the double of A's share and C must be Rs. 50 less than the double of B's share. The share of A will be:

Options

A. Rs. 19520
B. Rs. 1981.25
C. Rs. 2000
D. Rs. 2007.75

Answer

To solve the problem of dividing Rs. 13,950 among A, B, and C with the given conditions, we can follow these steps:

### Step 1: Define the shares
Let A's share be represented as \( A \). According to the problem:
- B's share is double of A's share, so \( B = 2A \).
- C's share is Rs. 50 less than double of B's share, so \( C = 2B - 50 \).

### Step 2: Substitute B's share into C's share
Since we know \( B = 2A \), we can substitute this into the equation for C:
\[ C = 2(2A) - 50 = 4A - 50 \]

### Step 3: Write the equation for the total amount
The total amount distributed among A, B, and C is Rs. 13,950. Therefore, we can write the equation:
\[ A + B + C = 13,950 \]
Substituting the expressions for B and C:
\[ A + 2A + (4A - 50) = 13,950 \]

### Step 4: Simplify the equation
Combine like terms:
\[ A + 2A + 4A - 50 = 13,950 \]
This simplifies to:
\[ 7A - 50 = 13,950 \]

### Step 5: Solve for A
Add 50 to both sides:
\[ 7A = 13,950 + 50 \]
\[ 7A = 14,000 \]
Now, divide both sides by 7:
\[ A = \frac{14,000}{7} = 2,000 \]

### Step 6: Conclusion
Thus, A's share is Rs. 2,000.