Question

The average age of three friends is 20 years and their ages are in the proportion 2:3:5, the age of the oldest friend is :

• A. 12 years
• B. 18 years
• C. 30 years
• D. 40 years

Answer 1

The Correct Option is C

To solve the problem of determining the age of the oldest friend, let's first understand the given data and perform step-by-step calculations.

The average age of three friends is given as 20 years. This means the total age of the three friends combined is:

\(3 \times 20 = 60\) years 

The ages are in the proportion 2:3:5, which means if the ages are \(2x\), \(3x\), and \(5x\), respectively.

To find the value of \(x\), we use the equation:

\(2x + 3x + 5x = 60\)

Simplifying this gives:

\(10x = 60\)

Solving for \(x\) gives:

\(x = \frac{60}{10} = 6\)

Now, we can calculate the age of the oldest friend, which is \(5x\):

\(5 \times 6 = 30\) years

Thus, the age of the oldest friend is 30 years.

Therefore, the correct option is:

• 30 years