A sum of money is divided among , A,B,C and D in the ratio of ` 3:5:9:13` respectively. If the share of C is `₹ 2412` more than the share of A, then what is the total amount of money of B and D togather ?

Options

A. `₹4422`
B. `₹ 7236`
C. `₹6030`
D. `₹ 4824`

Explanation

To solve the problem step-by-step, we will follow the given information and use the concept of ratios.

### Step 1: Understand the Ratios
The amounts received by A, B, C, and D are in the ratio of 3:5:9:13. We can represent their shares as:
- A's share = 3x
- B's share = 5x
- C's share = 9x
- D's share = 13x

### Step 2: Set Up the Equation
According to the problem, the share of C is ₹2412 more than the share of A. Therefore, we can set up the following equation:
\[ C's \, share - A's \, share = 2412 \]
Substituting the values:
\[ 9x - 3x = 2412 \]

### Step 3: Simplify the Equation
Now, simplify the equation:
\[ 6x = 2412 \]

### Step 4: Solve for x
To find the value of x, divide both sides by 6:
\[ x = \frac{2412}{6} \]
\[ x = 402 \]

### Step 5: Calculate Individual Shares
Now that we have the value of x, we can calculate the shares of A, B, C, and D:
- A's share = \(3x = 3 \times 402 = 1206\)
- B's share = \(5x = 5 \times 402 = 2010\)
- C's share = \(9x = 9 \times 402 = 3618\)
- D's share = \(13x = 13 \times 402 = 5226\)

### Step 6: Calculate Total Amount of B and D
Now, we need to find the total amount of money that B and D have together:
\[ Total \, of \, B \, and \, D = B's \, share + D's \, share \]
\[ Total \, of \, B \, and \, D = 2010 + 5226 = 7236 \]

### Final Answer
The total amount of money of B and D together is **₹ 7236**.

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