Question

kirti's father is five times as old as kirti after 5 years,father will be three times as old as kirti.find their present ages​

Answer 1

Answer :-

Present ages of Kirti and father are 5 years and 25 years respectively.

Explanation :-

Let the age of Kirti be x years

Age of Kirti's father = 5 times the age of Kirti = 5(x) = 5x years

Age of Kirti after 5 years = (x + 5) years

Age of Kirti's father after 5 years = (5x + 5) years

Given

Age of the father after 5 years = 3 times the age of Kirti

⇒ 5x + 5 = 3(x + 5)

⇒ 5x + 5 = 3x + 15

⇒ 5x - 3x = 15 - 5

⇒ 2x = 10

⇒ x = 10/2

⇒ x = 5

Present age of Kirti = x = 5 years

Present age of father= 5x = 5(5) = 25 years.

∴ Present ages of Kirti and father are 5 years and 25 years respectively.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Present age of Father = 25 years

Present age of Kirti = 5 years.

$\bold{\underline{\underline{Step\:-\:by\:-step\:explanation:}}}$

Given :-

• Kirti's father is five times as old as Kirti
• After 5 years,father will be three times as old as Kirti

To find :-

• Present age of Father
• Present age of Kirti

Solution :-

Let the present age of Father be x years.

Let the present age of Kirti be y years.

$\bold{\underline{\underline{As\:per\:first\:condition\::}}}$

• Kirti's father is five times as old as Kirti

$\rightarrwo$ $\bold{x\:=\:5y\:}$ ----> (1)

$\bold{\underline{\underline{As\:per\:second\:condition\::}}}$

• After 5 years,father will be three times as old as Kirti

Ages after 5 years :-

Father's age = x + 5 years

Kirti's age = y + 5 years

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

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

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

$\implies$ $\bold{x\:-\:3y\:=\:10}$ ----> 2

Substitute x = 5y in equation 2 for x,

$\implies$ $\bold{5y\:-3y\:=\:10}$

$\implies$ $\bold{2y\:=\:10}$

$\implies$ $\bold{y\:=\frac{10}{2}}$

$\implies$ $\bold{y\:=\:5}$

Substitute y = 5 in equation 1,

$\implies$$\bold{x\:=\:5y}$

$\implies$ $\bold{x\:=\:5\times\:5}$

$\implies$ $\bold{x\:=\:25\:years}$