The ratio between A, B and C is 2 : 3 : 7. If the share of B is Rs. 15,000, then find the difference between the shares of A and C.

Options

A. Rs. 30,000
B. Rs. 20,000
C. Rs. 25,000
D. Rs. 35,000

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Ratio
The ratio of the shares of A, B, and C is given as 2:3:7. This means:
- A's share = 2 parts
- B's share = 3 parts
- C's share = 7 parts

### Step 2: Calculate Total Parts
First, we need to find the total number of parts in the ratio:
Total parts = 2 + 3 + 7 = 12 parts.

### Step 3: Determine the Value of Each Part
We know that B's share is Rs. 15,000, which corresponds to 3 parts of the total. We can set up the equation:
\[ \frac{3}{12} \times X = 15,000 \]
Where \(X\) is the total amount shared among A, B, and C.

### Step 4: Solve for Total Amount (X)
To find \(X\), we can rearrange the equation:
\[ X = 15,000 \times \frac{12}{3} \]
Calculating this gives:
\[ X = 15,000 \times 4 = 60,000 \]

### Step 5: Calculate Individual Shares
Now that we know the total amount is Rs. 60,000, we can find the shares of A and C.

- **A's Share**:
\[ \text{A's share} = \frac{2}{12} \times 60,000 = 10,000 \]

- **C's Share**:
\[ \text{C's share} = \frac{7}{12} \times 60,000 = 35,000 \]

### Step 6: Find the Difference Between A's and C's Shares
Now we need to find the difference between the shares of A and C:
\[ \text{Difference} = \text{C's share} - \text{A's share} = 35,000 - 10,000 = 25,000 \]

### Final Answer
Therefore, the difference between the shares of A and C is Rs. 25,000.

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