Question : The ratio of the father's age to his son's age is 5 : 3. The product of the numbers representing their ages is 960. The ratio of their ages after 6 years will be:
Option 1: 23 : 15
Option 2: 23 : 17
Option 3: 21 : 15
Option 4: 21 : 17
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Correct Answer: 23 : 15
Solution :
The ratio of the ages of father to his son = 5 : 3
Let the age of the father = $5x$
The age of the son = $3x$
Product of their ages = 960
⇒ $(5x)(3x) = 960$
⇒ $15x^2 = 960$
⇒ $x^2 = 64$
⇒ $x = 8$
So, the age of father = $5x$ = 5 × 8 = 40 years
⇒ The age of son = $3x$ = 3 × 8 = 24 years
The age of father and son after 6 years will be
⇒ Father's age = 40 + 6 = 46 years
⇒ Son's age = 24 + 6 = 30 years
⇒ The ratio of the ages of father to son = Father's age : Son's age = 46 : 30 = 23 : 15
Hence, the correct answer is 23 : 15.
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