Four years ago the average age of A ,B and C was 25 years .Five years ago the average age of B and C was 20 years .A's present age is

Options

A. 60 years
B. 37 years
C. 62 years
D. 15 years

Answer

To find A's present age, we will break down the problem step by step.

### Step 1: Calculate the sum of ages of A, B, and C four years ago.
Given that the average age of A, B, and C four years ago was 25 years, we can use the formula for average:

\[ \text{Average} = \frac{\text{Sum of Ages}}{\text{Number of People}} \]

From the question, we know:

\[ \text{Average} = 25 \quad \text{and} \quad \text{Number of People} = 3 \]

So, the sum of their ages four years ago is:

\[ \text{Sum of Ages} = \text{Average} \times \text{Number of People} = 25 \times 3 = 75 \text{ years} \]

### Step 2: Calculate the present sum of ages of A, B, and C.
Since this sum is from four years ago, we need to add the years that have passed (4 years for each person):

\[ \text{Present Sum of Ages} = \text{Sum of Ages (4 years ago)} + 4 \times 3 = 75 + 12 = 87 \text{ years} \]

### Step 3: Calculate the sum of ages of B and C five years ago.
According to the question, the average age of B and C five years ago was 20 years. Using the same average formula:

\[ \text{Average} = 20 \quad \text{and} \quad \text{Number of People} = 2 \]

Thus, the sum of their ages five years ago is:

\[ \text{Sum of Ages (B and C)} = 20 \times 2 = 40 \text{ years} \]

### Step 4: Calculate the present sum of ages of B and C.
To find their present ages, we add the years that have passed (5 years for each person):

\[ \text{Present Sum of Ages (B and C)} = 40 + 5 \times 2 = 40 + 10 = 50 \text{ years} \]

### Step 5: Set up the equation to find A's present age.
Now we have two equations:
1. Present Sum of Ages (A, B, C) = 87 years
2. Present Sum of Ages (B, C) = 50 years

We can express A's present age as:

\[ A + (B + C) = 87 \]

Substituting \(B + C\) from the second equation:

\[ A + 50 = 87 \]

### Step 6: Solve for A's present age.
Now, we can solve for A:

\[ A = 87 - 50 = 37 \text{ years} \]

### Final Answer:
A's present age is **37 years**.

---