Question

Aman's age is three times his son's age.ten years ago he was five times his son's age.find their present ages​

Answer 1

$\huge\boxed{ \mathfrak Solution}$

Let present age of Son = x years

∴ Present age of Aman = 3x years

Ten years ago Son's age = (x-10) years

Aman's age = (3x-10) years

According to the condition, we have

[Son's age (10 years ago)] 5 = [Aman's age (10 years ago)]

or (x -10) 5 = (3x -10)

or 5x - 50 = 3x - 10

Transposing (-50) to RHS and 3x to LHS, we have

5x - 3x = -10 + 50

or 2x = 40

or

$\large \: x = \large \: \frac{40}{2} = 20$

[Dividing both sides by 2]

and 3x = 3 × 20 = 60

∴ Son's present age = 20 years

Aman's present age = 60 years

Answer 2

Answer:

Aman is 60 years old,

&

His son is 20 years old,.

Step-by-step explanation:

Given :

Aman's age is three times his son's age.

Ten years ago he was five times his son's age.

find their present ages​,..

Solution :

Statement 1 :

Aman's age is three times his son's age.

Ten years ago he was five times his son's age.

__

Let aman's age be $x$,.

Then his son's age would be $\frac{x}{3}$

Statement 2 :

Ten years ago he was five times his son's age.

aman's present age is $x$,.

⇒ 10 years ago, his age would be $x-10$

⇒ 10 years ago, his son's age would be $\frac{x}{3} -10$

⇒ 10 years ago, his son's age would be $\frac{x-10}{5}$

___

⇒ $\frac{x}{3} -10 = \frac{x-10}{5}$

⇒ $\frac{x-30}{3} = \frac{x-10}{5}$

⇒ $5(x-30) = 3(x-10)$

⇒ $5x-150 = 3x-30$

⇒ $5x-3x = -30+150$

⇒ $2x = 120$

⇒ $x = \frac{120}{2} = 60$

∴ The present age of Aman is 60 years.

Present age of son = $\frac{x}{3} = \frac{60}{3} = 20$

∴ The present age of son is 20 years.