Question

Five years hence,a man's age will be three times the age of his son.Five years ago, the man was seven times as old as his son.Find their present ages.

Answer 1

let present age of man

and son be x and y respectively

after 5 year

son age =y+5

father age =x+5

3(y+5)=x+5

3y-x=-10.........(1)

five years ago

son age y-5

father age x-5

7(y-5)=x-5

7y-x=30.......(2)

from (1) and (2)

4y=40

y=10 years

put the value in one then we get

x=40 years

Answer 2

Answer:

Step-by-step explanation:

Given :-

Five years hence, a man's age will be three times the age of his son.

Five years ago, the man was seven times as old as his son.

To Find  :-

Their Present ages

Solution :-

Let the present age of the man be x years

And His son's  be y years.  

1st Equation :-

After 5 years man’s age = x + 5  

After 5 years ago son’s age = y + 5  

As per the question  

⇒ x + 5 = 3(y + 5)

⇒ x – 3y = 10 ……………(i)  

2nd Equation

5 years ago man’s age = x – 5  

5 years ago son’s age = y – 5  

As per the question

⇒ x – 5 = 7(y – 5)

⇒ x – 7y = -30 …….(ii)

Subtracting (ii) from (i), we have  

⇒ 4y = 40  

⇒ y = 10  

Putting y value in Eq (i)

⇒ x – 3y = 10

⇒ x – 3 × 10 = 10  

⇒ x = 10 + 30

⇒ x = 40

Hence, man’s present age = 40 years and son’s present age = 10 years.