A sum of money is divided among A,B,C and D in the ratio of 3:4:9:10 respectively.If the share of C is Rs 2580/- more then the share of B,then what is the total amount of money of A and D together?

Options

A. Rs 5676
B. Rs 6192
C. Rs 6708
D. Rs 7224

Answer

To solve the problem step by step, we will follow the given ratios and the information provided about the shares of A, B, C, and D.

### Step 1: Define the shares based on the ratio
The shares of A, B, C, and D are given in the ratio of 3:4:9:10. We can express their shares in terms of a variable \( k \):
- Share of A = \( 3k \)
- Share of B = \( 4k \)
- Share of C = \( 9k \)
- Share of D = \( 10k \)

### Step 2: Set up the equation based on the information given
According to the problem, the share of C is Rs 2580 more than the share of B. We can write this as:
\[ 9k = 4k + 2580 \]

### Step 3: Solve for \( k \)
Now, we will solve the equation:
1. Subtract \( 4k \) from both sides:
\[ 9k - 4k = 2580 \]
\[ 5k = 2580 \]
2. Divide both sides by 5:
\[ k = \frac{2580}{5} \]
\[ k = 516 \]

### Step 4: Calculate the shares of A and D
Now that we have \( k \), we can calculate the shares of A and D:
- Share of A = \( 3k = 3 \times 516 = 1548 \)
- Share of D = \( 10k = 10 \times 516 = 5160 \)

### Step 5: Find the total amount of money of A and D together
To find the total amount of money A and D together, we add their shares:
\[ \text{Total of A and D} = \text{Share of A} + \text{Share of D} \]
\[ = 1548 + 5160 = 6708 \]

### Final Answer
The total amount of money of A and D together is Rs 6708.

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