Question

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.​

Answer 1

Answer  

Father's age =40 years, Son's age =10 years

Let the father present age =x years  and son present age =y years

According to the first condition

5 years later father will be (x+5) years old and son will be (y+5) years old.

⇒x+5=3(y+5)

⇒x+5=3y+15⇒x=3y+10....eq1

According to the second condition

5 years ago father was (x−5) years old and son was (y−5) years old.

⇒x−5=7(y−5)

⇒x−5=7y−35

⇒x−7y=−30....eq2

Put  the value of x from eq1

⇒3y+10−7y=−30⇒−4y=−40⇒y=10

Put y=10 in eq1

⇒x=3×10+10=40

 

Hence, Father present age =40 years

Son present age =10 years

Explanation:

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Answer 2

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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