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**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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Team Careers360 18th Jan, 2024

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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= 40years

⇒The age of son = $3x$ = 3 × 8 = 24years

The age of father and son after 6years will be

⇒Father's age = 40 + 6= 46years

⇒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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