Question

Father is 5 times as old as his son. The square of the sum of their ages is 5184. The age of the father is

• A. 67 years
• B. 60 years
• C. 66 years
• D. 70 years

Hint:

Since the father is 5 times as old as his son, his age must be a multiple of 5.
Looking at the options, only \(60\) and \(70\) are multiples of 5.
If Father = \(60\), then Son = \(12\). Sum = \(72\), and \(72^2 = 5184\), which works perfectly!

Answer 1

The Correct Option is B

Step 1: Set up the age relationship.
Let son's age = s. Then father's age = 5s, and sum of their ages = s + 5s = 6s.
Step 2: Apply the given condition.
Square of sum = (6s)^2 = 36s^2 = 5184. Therefore s^2 = 144 and s = 12.
Step 3: Find father's age.
Father's age = 5 x 12 = 60 years. Verify: (12 + 60)^2 = 72^2 = 5184.
\[ \boxed{60} \]