# Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was 7 times of his son. Find their present ages?

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Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was 7 times  of his son. Find their present ages?

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Solution: Let us assume Jacob’s current age is x and his son’s current age is y.

Five years hence, Jacob’s age = x + 5 and his son’s age = y + 5

As per question;

x + 5 = 3(y + 5)

Or, x + 5 = 3y + 15

Or, x = 3y + 15 – 5 = 3y + 10

Five years ago, Jacob’s age = x – 5 and his son’s age = y – 5

As per question;

x – 5 = 7(y – 5)

Or, x – 5 = 7y – 35

Or, x = 7y – 35 + 5 = 7y – 30

Substituting the value of x from first equation in this equation, we get;

3y + 10 = 7y – 30

Or, 3y + 10 + 30 = 7y

Or, 7y – 3y = 40

Or, 4y = 40

Or, y = 10

Substituting the value of y in first equation, we get;

x = 3y + 10

Or, x = 3 x 10 + 10 = 40

Hence, Jacob’s age = 40 years and son’s age = 10 years