Question : Directions: The age of the father is twice that of the elder son. After ten years, the age of the father will be three times that of the younger son. If the difference in ages of the two sons is 15 years, the age of the father is?
Option 1: 70 years
Option 2: 55 years
Option 3: 50 years
Option 4: 60 years
Correct Answer: 50 years
Solution :
Let the present age of the elder son be y years, then the father's present age will be 2y years.
Ten years later, the father's age = 2y + 10, and that is 3 times that of the younger son.
So, 10 years later, the younger son's age is $\frac{2y+10}{3}$.
The age difference between the two sons is 15 years.
⇒ $(y+10)-(\frac{2y+10}{3})=15$
⇒ $y-(\frac{2y+10}{3})=5$
Now, multiply the given equation by 3 –
⇒ 3y – (2y + 10) = 15
⇒ 3y – 2y – 10 = 15
⇒ y = 15 + 10 = 25
The age of the father is 25 × 2 = 50 years.
So, the age of the father is 50 years. Hence, the third option is correct.
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