The ages of A, B and C together total 185 years. B is twice as old as A and C is 17 years older than A. Then the respective ages of A, B and C are-

Options

A. 40,86 and 59 years
B. 42,80 and 59 years
C. 40,80and 65 years
D. None of these

Answer

To solve the problem of finding the ages of A, B, and C, we can follow these steps:

### Step 1: Define the variables
Let:
- A's age = \( x \)
- B's age = \( y \)
- C's age = \( z \)

### Step 2: Set up the equations based on the problem statement
From the problem, we have the following information:
1. The total age of A, B, and C is 185 years:
\[ x + y + z = 185 \]
2. B is twice as old as A:
\[ y = 2x \]
3. C is 17 years older than A:
\[ z = x + 17 \]

### Step 3: Substitute the values of y and z in the total age equation
Now we can substitute the values of \( y \) and \( z \) from the second and third equations into the first equation:
\[ x + (2x) + (x + 17) = 185 \]

### Step 4: Simplify the equation
Combine like terms:
\[ x + 2x + x + 17 = 185 \]
\[ 4x + 17 = 185 \]

### Step 5: Solve for x
Subtract 17 from both sides:
\[ 4x = 185 - 17 \]
\[ 4x = 168 \]
Now divide by 4:
\[ x = \frac{168}{4} = 42 \]

### Step 6: Find the ages of B and C
Now that we have A's age:
- A's age \( x = 42 \)
- B's age \( y = 2x = 2 \times 42 = 84 \)
- C's age \( z = x + 17 = 42 + 17 = 59 \)

### Step 7: Conclusion
Thus, the respective ages of A, B, and C are:
- A = 42 years
- B = 84 years
- C = 59 years

### Final Answer
The ages of A, B, and C are 42 years, 84 years, and 59 years, respectively.

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