Question : The average age of a man and his son is 55 years. The ratio of their ages is 7 : 4, respectively. What will be the ratio of their ages after 6 years?
Option 1: 1 : 2
Option 2: 12 : 7
Option 3: 25 : 17
Option 4: 38 : 23
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Correct Answer: 38 : 23
Solution :
Let the age of man and son be $7x$ and $4x$ respectively.
Average age = $\frac{7x+4x}{2}$
⇒ $55= \frac{11x}{2}$
⇒ $x= 10$
Age of man after 6 years = $7x+6$ = 76
Age of son after 6 years = $4x+6$ = 46
Required ratio = 76 : 46 = 38 : 23
Hence, the correct answer is 38 : 23.
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