A sum of money is divided amongst A, B, C and D in the ratio of 3 : 7 : 9 : 13. If the share of B is X 4872, then what will be the total amount of money of Aand C together?

Options

A. X 8352
B. X 6998
C. X 9784
D. X 7456

Answer

To solve the problem step by step, we will follow the given ratio and the share of B to find the total amount of money for A and C together.

### Step 1: Understand the ratio
The ratio of the shares of A, B, C, and D is given as:
- A : B : C : D = 3 : 7 : 9 : 13

### Step 2: Assign variables based on the ratio
Let the common multiplier be \( k \). Then we can express the shares of A, B, C, and D as:
- A's share = \( 3k \)
- B's share = \( 7k \)
- C's share = \( 9k \)
- D's share = \( 13k \)

### Step 3: Use the given information about B's share
We know that B's share is \( 4872 \). Thus, we can set up the equation:
\[ 7k = 4872 \]

### Step 4: Solve for \( k \)
To find \( k \), we divide both sides of the equation by 7:
\[ k = \frac{4872}{7} \]

Calculating this gives:
\[ k = 696 \]

### Step 5: Calculate A's and C's shares
Now that we have \( k \), we can find the shares of A and C:
- A's share = \( 3k = 3 \times 696 = 2088 \)
- C's share = \( 9k = 9 \times 696 = 6264 \)

### Step 6: Find the total amount of A and C together
Now, we add A's and C's shares together:
\[ \text{Total of A and C} = A's \, share + C's \, share = 2088 + 6264 = 8352 \]

### Final Answer
The total amount of money of A and C together is **8352**.

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