Question

Five years hence, the age of Jacob will be three times that of his son. Five years ago,Jacob's age was seven times that of his son. What are their present ages? ​

Answer 1

Let present age of Jacob= x years

Let present age of son= y years

After 5 years

x+5= 3(y+5)

x+5= 3y+15

x= 3y+10

Before 5 years

x-5= 7(y-5)

x-5= 7y-35

x= 7y-30

3y+10= 7y-30

40= 4y

y= 10 years

x= 40 years

Answer 2

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Given :-

• The age of Jacob will be three times that of his son.

• Five years ago, Jacob's age was seven times that of his son.

To find :-

• Their present ages.

Let the present age of Jacob be be x year                  

And the present Age of his son be be y year    

             

Five years Ago,

Jacob’s age will be = x + 5 year                  

Age of his son will be = y + 5 year      

           

According to the Question,

⇒ x + 5 = 3(y + 5)                  

Adding 5 to both side,                  

⇒ x = 3y + 15 - 5                  

⇒ x = 3y + 10 … (i)                  

Five years ago,                  

Jacob’s age= x - 5 year                  

His son’s age = y - 5 year                  

Jacob’s age was seven times that of his son                  

⇒ x - 5 = 7(y - 5)                  

Putting the value of x from equation (i) we get                  

⇒ 3y + 10 - 5 = 7y - 35                  

⇒ 3y + 5 = 7y – 35                  

⇒ 3y - 7y = - 35 - 5                  

⇒ -4y = - 40                  

⇒ y = - 40/-4                  

⇒ y = 10 year                  

Putting the value of y in equation we get                  

⇒ x = 3 × 10 + 10                  

⇒ x = 40 years        

         

Present age of Jacob = 40 years,

Present age of his son = 10 years.

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