Question

Five years hence, the age of jacob will be three times of his son. five years ago, jacob's age was seven times that of his son. What are their present ages?
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Answer 1

Answer:

The present age of Jacob is 40 years

The present age of Jacob's Son is 10 years

Step-by-step explanation:

Let,

The present age of Jacob = x

The present age of Jacob's Son = y

After 5 years,

The age of Jacob = x + 5

The age of Jacob's Son = y + 5

Also,

Jacob will be 3 times of his son's age

So,

⇒ x + 5 = 3 (y + 5)

⇒ x + 5 = 3y + 15

⇒ x = 3y + 15 - 5

⇒ x = 3y + 10 ------------------(i)

5 years ago,

The age of Jacob = x - 5

The age of Jacob's Son = y - 5

Also,

Jacob's age was 7 times that of his son

So,

⇒ x - 5 = 7 (y - 5)

⇒ x - 5 = 7y - 35

⇒ x = 7y - 35 + 5

⇒ x = 7y - 30

★ Putting value of x from equation (i)

⇒ 3y + 10 = 7y - 30

⇒ 3y - 7y = -30 - 10

⇒ - 4y = - 40

⇒ 4y = 40

⇒ y = 40 / 4

⇒ y = 10

★ x = 3y + 10

⇒ 3 (10) + 10

⇒ 30 + 10

⇒ 40

⇒ x = 40

Therefore,

The present age of Jacob is 40 years

The present age of Jacob's Son is 10 years

Answer 2

$\sf\large\underline{Let:}$

$\sf{\implies The\: present\:age\:of\:Jacob=x}$

$\sf{\implies The\:present\:age\:of\:his\:son=y}$

$\sf\large\underline{To\:Find:}$

$\sf{\implies The\:present\:age\:_{(Jacob\:and\:his\:son)}=?}$

$\sf\large\underline{Solution:}$

• To find the present age of Jacob and his son at first we have to set up equation as per the given clue in the question then solve those equation after that we get the present age of Jacob and his son.]

$\sf\small\underline{Given\:in\: case\:(i)}$

• Five years hence, the age of jacob will be three times of his son.]

$\tt{\implies x+5=3(y+5)}$

$\tt{\implies x+5=3y+15}$

$\tt{\implies x-3y=15-5}$

$\tt{\implies x-3y=10----(i)}$

$\sf\small\underline{Given\:in\: case\:(ii)}$

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

$\tt{\implies x-5=7(y-5)}$

$\tt{\implies x-5=7y-35}$

$\tt{\implies x-7y=-35+5}$

$\tt{\implies x-7y=-30-----(ii)}$

Solve equation (i) and (ii) here]

$\tt{\implies x-3y=10}$

$\tt{\implies x-7y=-30}$

• By solving we get,here]

$\tt{\implies 4y=40\implies y=10}$

• Now putting the value of y=10 in eq (i)]

$\tt{\implies x-3y=10}$

$\tt{\implies x-3(10)=10}$

$\tt{\implies x-30=10}$

$\tt{\implies x=10+30\implies x=40}$

$\sf\large{Hence,}$

$\bf{\implies The\: present\:age\:_{(Jacob)}=40\: years}$

$\bf{\implies The\: present\:age\:_{(his\:son)}=10\: years}$