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Five Years Hence, The Age Of Jacob Will Be Three Times That Of His Son. Five Year Ago, Jacob’s Age Was Seven Times That Of His Son. What Are Their Present Ages?​

Answer 1

Answer :

• Jacob's present age = 40 years
• Jacob's son's present age = 10 years

Solution :

Given :

• After five years, 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 :

• The present age of Jacob
• The present age of Jacob's son

Required Solution :

Let,

• The present age of Jacob = x years
• The present age of Jacob's son = y years

Their ages after five years :

= Jacob's age after 5 years = x + 5 years

= Jacob's son's age after 5 years = y + 5 years

According to the first condition given,

= Jacob's age = 3(Jacob's son's age)

= x + 5 = 3(y + 5)

= x + 5 = 3y + 15

= x - 3y = 15 - 5

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

Their ages before 5 years :

= Jacob's age before 5 years = x - 5 years

= Jacob's son's age before 5 years = y - 5 years

According to the second condition given,

= Jacob's age = 7(Jacob's son's age)

= x - 5 = 7(y - 5)

= x - 5 = 7y - 35

= x - 7y = - 35 + 5

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

Solving (1) and (2) :

⠀⠀⠀⠀⠀⠀⠀⠀x - 3y = 10

⠀⠀⠀⠀⠀⠀⠀⠀x - 7y = - 30

⠀⠀⠀⠀⠀⠀⠀⠀-⠀+⠀⠀⠀+

⠀⠀⠀⠀⠀⠀______________

⠀⠀⠀⠀⠀⠀⠀⠀⠀4y = 40

⠀⠀⠀⠀⠀⠀______________

= 4y = 40

= y = 40/4

= y = 10

• The value of y = 10

Substituting the value of y in equation (1) $:$

= x - 3y = 10

= x - 3(10) = 10

= x - 30 = 10

= x = 10 + 30

= x = 40

• The value of x = 40

The age of Jacob and his son :

⇒ Jacob's present age = x years

⇒ Jacob's present age = 40 years

⇒ Jacob's son's present age = y years

⇒ Jacob's son's present age = 10 years

Answer 2

Answer:

Solution:

Let 'x' be the present age of Jacob and 'y' be the age of his son.

As per question,

⟹ x + 5 = 3( y + 5)

⟹ x+5 = 3y+15

⟹ x = 3y +10 ...(1)

And,

⟹ x - 5 = 7( y - 5)

⟹ x-5 = 7y -35

⟹ x = 7y -30 ...(2)

Adding (1) and (2),

⟹ 2x = 7y -30 +5y-10

⟹ 2x = 12y - 40

⟹ x = 6y - 20 ...(3)

Putting equation (3) in (1),

⟹ x = 3y+10

⟹ 6y-20 = 3y+10

⟹ 3y = 30

⟹ y = 10

Putting y = 10 in (1)

⟹ x = 3y + 10

⟹ x = 3×10+10

⟹ x = 40

Therefore,

• Present age of Jacob is 40 years
• present age of his son is 10 years [tex][/tex]