A, B and C have amounts in the ratio of 3: 4: 5. First B gives 1/4th to A and 1/4th to C then C gives 1/6th to A. Find the final ratio of amount of A, B and C, respectively :

Options

A. 0.16880787037037
B. 0.21114583333333
C. 0.25280092592593
D. 0.20978009259259

Answer

To solve the problem step-by-step, we will first express the amounts of A, B, and C based on the given ratio and then apply the transactions as described in the question.

### Step 1: Assign Initial Amounts
Given the ratio of A, B, and C is 3:4:5, we can assign their amounts as follows:
- Let the common multiple be \( x \).
- Amount of A = \( 3x \)
- Amount of B = \( 4x \)
- Amount of C = \( 5x \)

### Step 2: B Gives 1/4th to A and C
B gives 1/4th of his amount to A and 1/4th to C.
- Amount given to A = \( \frac{1}{4} \times 4x = x \)
- Amount given to C = \( \frac{1}{4} \times 4x = x \)

After these transactions:
- Amount of A = \( 3x + x = 4x \)
- Amount of B = \( 4x - x - x = 2x \) (since B gave away \( 2x \))
- Amount of C = \( 5x + x = 6x \)

### Step 3: C Gives 1/6th to A
C gives 1/6th of his amount to A.
- Amount given to A = \( \frac{1}{6} \times 6x = x \)

After this transaction:
- Amount of A = \( 4x + x = 5x \)
- Amount of C = \( 6x - x = 5x \)

### Step 4: Final Amounts
Now we have the final amounts:
- Amount of A = \( 5x \)
- Amount of B = \( 2x \)
- Amount of C = \( 5x \)

### Step 5: Calculate the Final Ratio
The final ratio of the amounts of A, B, and C is:
- A : B : C = \( 5x : 2x : 5x \)

To simplify this ratio, we can divide each term by \( x \):
- A : B : C = \( 5 : 2 : 5 \)

### Final Answer
The final ratio of the amounts of A, B, and C is **5 : 2 : 5**.

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