Question

Five years ago a man was seven times as old as his son. Five years hence, the father will be
three times as old as his son. Find their present ages.​

Answer 1

Given :

• Five years ago a man was seven times as old as his son.
• Five years hence, the father will be
• three times as old as his son.

To find :

• The present age of father and his son.

Solution :

Let,

• Present age of son = x years
• Present age of father = y years

Their ages before 5 years ::

⇒ Age of son = x - 5 years

⇒ Age of father = y - 5 years

According to the question,

⇒ Father's age = 7(Age of his son)

⇒ y - 5 = 7(x - 5)

⇒ y - 5 = 7x - 35

⇒ - 5 + 35 = 7x - y

⇒ 30 = 7x - y

⇒ 7x - y = 30 -----(1)

Their ages after 5 years ::

⇒ Age of son = x + 5 years

⇒ Age of father = y + 5 years

According to the question,

⇒ Father's age = 3(Son's age)

⇒ y + 5 = 3(x + 5)

⇒ y + 5 = 3x + 15

⇒ 5 - 15 = 3x - y

⇒ - 10 = 3x - y

⇒ 3x - y = - 10 -----(2)

Solving (1) and (2) :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀ 7x - y = 30

⠀⠀⠀⠀⠀⠀⠀⠀⠀3x - y = - 10

⠀⠀⠀⠀⠀⠀⠀⠀⠀(-)⠀(+)⠀(+)

⠀⠀⠀⠀⠀⠀⠀⠀_____________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀4x = 40

⠀⠀⠀⠀⠀⠀⠀⠀ _____________

⇒ 4x = 40

⇒ x = 40/4

⇒ x = 10

Substitute the value of x in equation '1' :-

⇒ 7x - y = 30

⇒ 7(10) - y = 30

⇒ 70 - y = 30

⇒ - y = 30 - 70

⇒ - y = - 40

⇒ y = 40

Therefore,

• The present age of son = x = 10 years
• The present age of father = y = 40 years

Answer 2

Given : Five years ago a man was seven times as old as his son & Five years hence, the father will be three times as old as his son. Find their present ages.

To Find : Find the present age of son and his father ?

_________________________

Solution : Five years ago a man was seven times as old as his son.

$~$

$\pmb{\sf{\underline{According ~to ~the~ Given ~Question~:}}}$

$~$

Five year's ago : -

• Let the age of son be x years
• Age of father = 7x

So,

• present age of son = x + 5
• present age of father = 7x + 5

Five years hence, the father will be three times as old as his son.

After 5 year's : -

• Age of son = x + 5 + 5 = x + 10
• Age of father = 7x + 10

But age of father is 3 times age of son .

So,

$\qquad\qquad{\sf:\implies{7x~ + ~10 ~= ~3\bigg(x ~+ ~10\bigg)}}$

$\qquad\qquad{\sf:\implies{7x~ + ~10 ~= ~3x~+~30}}$

$\qquad\qquad{\sf:\implies{7x~ - ~3x ~= ~30~-~10}}$

$\qquad\qquad{\sf:\implies{4x~=~12}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\blue{x~=~5}}}}}$★

$~$

• Present age of father : -

$\qquad\qquad{\sf:\implies{7x~+~5}}$

$\qquad\qquad{\sf:\implies{7~×~5~+~5}}$

$\qquad\qquad{\sf:\implies{35~+~5}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\purple{40~=~year's}}}}}$★

$~$

• Present age of son : -

$\qquad\qquad{\sf:\implies{x~+~5}}$

$\qquad\qquad{\sf:\implies{5~+~5}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\pink{10~=~year's}}}}}$★

$~$

Hence,

• $\underset{\blue {\bf Required\ Answer}}{\underbrace{\boxed{\frak{\pink{\dfrac{Present ~age~ of ~Son~=~10~year's}{Present ~age~ of ~Father~=~40~year's}}}}}}$