Question : Directions: The sum of the ages of a father and a son presently is 70 years. After 10 years, the son's age is exactly half that of the father. What are their ages now?
Option 1: 45 years, 25 years
Option 2: 50 years, 20 years
Option 3: 47 years, 23 years
Option 4: 50 years, 25 years
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Correct Answer: 50 years, 20 years
Solution : Let the father's present age be A, and his son's present age be B.
As per the given information,
The sum of the father's present age and his son's present age is 70 years ⇒ A + B = 70
After 10 years, father's age = (A + 10), and his's son's age = (B + 10)
Also, after 10 years, Son's age will be half the of his father's age, i.e., (A + 10) = 2 × (B + 10)
⇒ A + 10 = 2B + 20
⇒ A = 2B + 20 – 10
⇒ A = 2B + 10
So, substitute the value of A in equation A + B = 70, thus, the equation becomes –
⇒ 2B + 10 + B = 70
⇒ 3B = 70 – 10 = 60
⇒ B = 60 ÷ 3 = 20
Therefore, the Son's present age is 20 years, and the Father's present age is 50 years. Hence, the second option is correct.
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