Ten years ago, average age of A and B was 20 years. Average age of A, B and C is 30 years today. How old C will be after 5 years?

Options

A. (a) 20 years
B. (b) 30 years
C. (c) 35 years
D. (d) 55 years

Explanation

To solve the problem step by step, we will first determine the ages of A and B, then find the age of C, and finally calculate how old C will be in 5 years.

### Step 1: Determine the ages of A and B 10 years ago.
Given that the average age of A and B 10 years ago was 20 years, we can set up the equation:
\[ \text{Average age of A and B} = \frac{A_{10\text{ years ago}} + B_{10\text{ years ago}}}{2} = 20 \]
This implies:
\[ A_{10\text{ years ago}} + B_{10\text{ years ago}} = 20 \times 2 = 40 \]

### Step 2: Calculate the current ages of A and B.
Since this was 10 years ago, we add 10 years to their ages:
\[ A + B = 40 + 20 = 60 \]

### Step 3: Determine the average age of A, B, and C today.
We know that the average age of A, B, and C today is 30 years:
\[ \text{Average age of A, B, and C} = \frac{A + B + C}{3} = 30 \]
This implies:
\[ A + B + C = 30 \times 3 = 90 \]

### Step 4: Substitute the value of A + B into the equation.
From Step 2, we have \(A + B = 60\). We can substitute this into the equation from Step 3:
\[ 60 + C = 90 \]
Now, solving for C:
\[ C = 90 - 60 = 30 \]

### Step 5: Calculate how old C will be in 5 years.
To find out how old C will be in 5 years, we add 5 to C's current age:
\[ C + 5 = 30 + 5 = 35 \]

### Final Answer:
C will be 35 years old after 5 years.

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