Rs. 11250 are divided among A,B and C so that A may receive one half as much as B and C together receive and B receives one -fourth of what A and C together receive. The share of A is more than that of B by:

Options

A. Rs. 2500
B. Rs. 1500
C. Rs. 1800
D. Rs. 650

Answer

To solve the problem step by step, we need to set up equations based on the relationships given in the question.

### Step 1: Define the variables
Let:
- A = share of A
- B = share of B
- C = share of C

### Step 2: Set up the equations based on the problem statement
According to the problem:
1. A receives one half as much as B and C together:
\[ A = \frac{1}{2}(B + C) \quad \text{(Equation 1)} \]
2. B receives one-fourth of what A and C together receive:
\[ B = \frac{1}{4}(A + C) \quad \text{(Equation 2)} \]
3. The total amount is Rs. 11,250:
\[ A + B + C = 11250 \quad \text{(Equation 3)} \]

### Step 3: Express C in terms of A and B
From Equation 1, we can express C:
\[ C = 2A - B \quad \text{(Substituting into Equation 1)} \]

### Step 4: Substitute C into Equation 3
Substituting C into Equation 3 gives:
\[ A + B + (2A - B) = 11250 \]
This simplifies to:
\[ 3A = 11250 \]
Thus, we find:
\[ A = \frac{11250}{3} = 3750 \]

### Step 5: Find B using Equation 1
Now substitute A back into Equation 1 to find B:
\[ 3750 = \frac{1}{2}(B + C) \]
From this, we can express B + C:
\[ B + C = 2 \times 3750 = 7500 \quad \text{(Equation 4)} \]

### Step 6: Substitute B into Equation 2
Now we can substitute B into Equation 2:
\[ B = \frac{1}{4}(3750 + C) \]
Substituting B from Equation 4:
\[ 7500 - C = \frac{1}{4}(3750 + C) \]
Multiplying both sides by 4 to eliminate the fraction:
\[ 4(7500 - C) = 3750 + C \]
This simplifies to:
\[ 30000 - 4C = 3750 + C \]
Combining like terms gives:
\[ 30000 - 3750 = 5C \]
Thus:
\[ 26250 = 5C \quad \Rightarrow \quad C = \frac{26250}{5} = 5250 \]

### Step 7: Find B using Equation 4
Now we can find B using Equation 4:
\[ B + 5250 = 7500 \quad \Rightarrow \quad B = 7500 - 5250 = 2250 \]

### Step 8: Find the difference between A and B
Finally, we need to find how much more A receives than B:
\[ A - B = 3750 - 2250 = 1500 \]

### Final Answer
The share of A is more than that of B by Rs. 1500.

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