Question

5 years hence the age of jacob will be 3 times that of his son five tears ago jacobs age will be seven times that of his son what are their present ages

Answer 1

HI Jitu ,

Let j be Jacob' present age
Let s be Jacob's son's age

NOTE :"5 years hence" means after 5 years

Given
j+5 = 3(s+5)
j-5 + 7(s-5)

solving above equations we get
s = 10
j = 40

so Jacob's age is 40 years and his son's age is 10 years.

Hope it helped.
Let me know if any doubts.
Cheers !!!

Answer 2

Let x be the present age of Jacobs son and y be the present age of Jacob. 5 year hence it has relation :

(y + 5) = 3(x + 5)

y + 5 = 3x + 15

3x - y + 10 = 0 ............... (Eqn 1)

5 years ago it has relation :-

(y - 5) = 7(x - 5)

7x - y - 30 = 0 ............ (Eqn 2)

From Equation 1

Y = 3x + 10 .......... (Eqn 3)

On substituting the value of y in Eqn. 2 we get :-

7x – (3x + 10) – 30 = 0

4x – 40 = 0

x = 10

On substituting x = 10 in eqn 3

y = 3 × 10 + 10

y = 40

Hence the present age of Jacob = 40 years and son age = 10 years