Average of present age of A, B and C is 31 years and C is one year older than A. If ratio between present age of B and C is 19:14 then find age of B?

Options

A. A)35 years
B. B)38 years
C. C)34 years
D. D)32 years

Answer

To solve the problem step by step, we will use the information given in the question.

### Step 1: Understand the given information
- The average age of A, B, and C is 31 years.
- C is one year older than A.
- The ratio of the ages of B and C is 19:14.

### Step 2: Set up the equations
Let the present age of C be represented as \( 14k \) and the present age of B as \( 19k \) (since the ratio of B to C is 19:14).

Since C is one year older than A, we can express A's age as:
\[ A = C - 1 = 14k - 1 \]

### Step 3: Calculate the total age
The total age of A, B, and C can be expressed as:
\[ A + B + C = (14k - 1) + (19k) + (14k) \]

### Step 4: Simplify the total age
Combining the ages:
\[ A + B + C = 14k - 1 + 19k + 14k = 47k - 1 \]

### Step 5: Set up the equation for average age
The average age of A, B, and C is given as 31 years. Therefore:
\[ \frac{A + B + C}{3} = 31 \]

Multiplying both sides by 3 gives:
\[ A + B + C = 93 \]

### Step 6: Set the two expressions for total age equal
Now we can set the two expressions for total age equal to each other:
\[ 47k - 1 = 93 \]

### Step 7: Solve for k
Adding 1 to both sides:
\[ 47k = 94 \]

Now, divide by 47:
\[ k = 2 \]

### Step 8: Find the age of B
Now that we have the value of \( k \), we can find the age of B:
\[ B = 19k = 19 \times 2 = 38 \]

### Conclusion
The present age of B is 38 years.

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