Five years hence, father's age will be three times the age of his son. Five years ago, father was seven times as old as his son. Find their present ages.
Answers
Step-by-step explanation:
Given :
Five years hence, father's age will be three times the age of his son.
Five years ago, father was seven times as old as his son.
To find :
Their present ages.
Solution :
Let the present ages of the Father and the Son be x and y years.
1st condition : [Hence/Future]
=> After 5 years man’s age = x + 5
=> After 5 years ago son’s age = y + 5
According to the question :
=> x + 5 = 3(y + 5)
=> x + 5 = 3y + 15
=> x - 3y = 10 -- (1)
2nd condition : [Ago/Past]
=> 5 years ago man’s age = x - 5
=> 5 years ago son’s age = y - 5
According to the question :
=> x - 5 = 7(y - 5)
=> x - 7y = -30 -- (2)
Subtracting (2) from (1) :
=> x - 7y = -30
=> x - 3y = 10
- 4y = 40
- y = 10
Substitute the value of y in (1) :
=> x - 3y = 10
=> x - 3(10) = 10
=> x - 30 = 10
=> x = 40
Therefore :
Father's present age = 40 years.
Son’s present age = 10 years.
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