A sum of Rs. 63 is divided among A,B,C in such a way that A gets Rs. 7 more than what B gets and gets Rs. 8 more than what C gets. The ratio of their shares is:

Options

A. `16:9:18`
B. `27:18:10`
C. `18:25:10`
D. None of these

Answer

To solve the problem of dividing Rs. 63 among A, B, and C with the given conditions, we can follow these steps:

### Step 1: Set up the equations based on the problem statement.
- Let the amount B receives be \( b \).
- According to the problem, A receives Rs. 7 more than B, so we can express A's share as:
\[ A = b + 7 \]
- Also, A receives Rs. 8 more than C, which gives us:
\[ A = c + 8 \]

### Step 2: Express C in terms of B.
From the second equation, we can express C in terms of A:
\[ c = A - 8 \]
Now substituting \( A = b + 7 \) into this equation:
\[ c = (b + 7) - 8 = b - 1 \]

### Step 3: Write the total amount equation.
The total amount distributed among A, B, and C is Rs. 63. Therefore, we can write:
\[ A + B + C = 63 \]
Substituting the expressions for A and C:
\[ (b + 7) + b + (b - 1) = 63 \]

### Step 4: Simplify the equation.
Combining like terms:
\[ 3b + 6 = 63 \]

### Step 5: Solve for B.
Subtract 6 from both sides:
\[ 3b = 57 \]
Now divide by 3:
\[ b = 19 \]

### Step 6: Find A and C.
Now that we have B's share, we can find A and C:
- For A:
\[ A = b + 7 = 19 + 7 = 26 \]
- For C:
\[ c = b - 1 = 19 - 1 = 18 \]

### Step 7: Write the ratio of their shares.
Now we have:
- A = 26
- B = 19
- C = 18

Thus, the ratio of their shares is:
\[ A : B : C = 26 : 19 : 18 \]

### Final Answer:
The ratio of their shares is \( 26 : 19 : 18 \).

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