A 's capital is equal to twice B's capital and B' s capital is three times C's capital .the ratio of the capital is

Options

A. (2:1:3)
B. (1:2:6)
C. (6:3:1)
D. (1:3:6)

Answer

To solve the problem step by step, we need to establish the relationships between the capitals of A, B, and C based on the information given.

### Step 1: Define the variables
Let:
- B's capital = x
- C's capital = y

### Step 2: Express A's capital in terms of B's capital
According to the problem, A's capital is twice B's capital. Therefore:
- A's capital = 2 * B's capital = 2x

### Step 3: Express B's capital in terms of C's capital
The problem states that B's capital is three times C's capital. Therefore:
- B's capital = 3 * C's capital = 3y

### Step 4: Set up the equations
From the definitions:
- We have B's capital as both x and 3y.
Thus, we can write:
- x = 3y

### Step 5: Substitute B's capital into A's capital
Now, substitute the value of x in A's capital:
- A's capital = 2x = 2(3y) = 6y

### Step 6: Write the ratio of A, B, and C's capitals
Now we have:
- A's capital = 6y
- B's capital = 3y
- C's capital = y

So, the ratio of A : B : C is:
- A : B : C = 6y : 3y : y

### Step 7: Simplify the ratio
To simplify the ratio, we can divide each term by y:
- A : B : C = 6 : 3 : 1

### Final Answer
Thus, the ratio of the capitals of A, B, and C is:
- **6 : 3 : 1**

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