Question : The ratio of a father's age to his son's age is 3 : 2 The product of the numbers representing their age is 486. The ratio of their ages after 5 years will be:
Option 1: 32 : 24
Option 2: 32 : 21
Option 3: 32 : 22
Option 4: 32 : 23
Correct Answer: 32 : 23
Solution :
Let the father’s age as $3x$ and the son’s age as $2x$.
According to the problem, the product of their ages is 486.
$⇒3x × 2x = 486$
$⇒ 6x^2 = 486$
$⇒ x^2 = 81$
$⇒x = 9$
So, the father’s current age = $3x$ = 27 years
The son’s current age = $2x$ = 18 years
After 5 years, the father will be 32 years old and the son will be 23 years old.
The ratio of their ages after 5 years will be 32 : 23.
Hence, the correct answer is 32 : 23.
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