Question

A father is 20 years older than the son in 5 years the father age will be 7years more then twice that of the son find their present age​

Answer 1

Given :

• A father is 20 years older than the son in 5 years
• The father age will be 7years more then twice that of the son

To Find :

• Pesent age of father and son

Solution :

Let present age of father and son be x and y years.

Father's age = Son age + 20

x = y + 20 ------------> (1)

After 5 years age of father = 2 ( After 5 years age of son ) + 7

x + 5 = 2 ( y + 5 ) + 7

x + 5 = 2y + 10 + 7

x - 2y = 12 ----------> (2)

Substitute the value of "x" in equation 2, we get

⇒ x - 2y = 12

⇒ y + 20 - 2y = 12

⇒ -y = 12 - 20

⇒ -y = -8

⇒ y = 8

Putting the value of "y" in equation 1, we get

⇒ x = y + 20

⇒ x = 8 + 20

⇒ x = 28

•°• Hence,

• Age of Father (x) = 28 years
• Age of Son (y) = 8 years

Answer 2

${\huge {\underline {\bf {\blue {Question}}}}}$

A father is 20 years older than the son in 5 years the father age will be 7years more then twice that of the son. Find their present age.

${\huge {\underline {\bf {\blue {Answer}}}}}$

Given :-

• A father is 20 years older than the son.
• In 5 years the father age will be 7 years more then twice that of the son.

To Find :-

• Present age of Father and the son.

Solution :-

Let, the age of son be "x"

the age of the father be "y"

According to the question

Father's age = Son's age + 20

y = x + 20 $~~~~~$ ---------------- (eq. 1)

After 5 years,

Age of son = x + 5

Age of Father = 2 ( age of son after 5 years ) + 7

$\implies$ ${\sf {y + 5 = 2 ( x + 5 ) + 7}}$

$\implies$ ${\sf {y + 5 = 2x + 10 + 7}}$

$\implies$ ${\sf {y + 5 = 2x + 17}}$

$\implies$ ${\sf {y - 2x = 17 - 5}}$

y - 2x = 12 $~~~~~$ ---------------- (eq. 2)

Substitute the value of "y" in eq. 2, we get

$\implies$ ${\sf {y - 2x = 12}}$

$\implies$ ${\sf {x + 20 -2x = 12}}$

$\implies$ ${\sf {-x = 12 - 20}}$

$\implies$ ${\sf { {\cancel {-} x = {\cancel {-} 8}}}}$

$\implies$ ${\underline {\boxed {\sf {x = 8}}}}$

Now, substitute the value of "x" in eq. 1, we get

$\implies$ y = x + 20

$\implies$ y = 8 + 20

$\implies$ ${\underline {\boxed {\sf {y = 28}}}}$

Hence,

${\underline {\purple {\sf {The~ present~ age~ of~ son~ = x = 8~ years}}}}$

${\underline {\purple {\sf {The~ present~ age~ of~ father~ = y = 28~ years.}}}}$