If a sum of money Is to be divided among A, B, C such that A's share is equal to twice B's share and B's share Is 4 times C's share, then their shares are In the ratio:

Options

A. `1:2:4`
B. `1:4:1`
C. `8:4:1`
D. `2:4:1`

Answer

To solve the problem step by step, we will define the shares of A, B, and C based on the relationships given in the question.

### Step 1: Define the shares
Let the share of C be \( C \).

### Step 2: Express B's share in terms of C's share
According to the problem, B's share is 4 times C's share:
\[ B = 4C \]

### Step 3: Express A's share in terms of B's share
It is also given that A's share is equal to twice B's share:
\[ A = 2B \]

### Step 4: Substitute B's share into A's share
Now, we can substitute the expression for B into the equation for A:
\[ A = 2(4C) = 8C \]

### Step 5: Write all shares in terms of C
Now we have:
- \( A = 8C \)
- \( B = 4C \)
- \( C = C \)

### Step 6: Write the ratio of A, B, and C
Now we can express the shares of A, B, and C in terms of C:
\[ A : B : C = 8C : 4C : C \]

### Step 7: Simplify the ratio
To simplify the ratio, we can divide each term by \( C \):
\[ A : B : C = 8 : 4 : 1 \]

### Conclusion
Thus, the shares of A, B, and C are in the ratio:
\[ \text{Ratio} = 8 : 4 : 1 \]