Question

five years ago, Amit was three times as Old as armaan. ten years later Amit would be twice as old as armaan. how old are they now?

Answer 1

Hello Mate!

Let the persent ages of Amit and Armaan be x and y respectively

5 years ago, there ages will be in equation :-

x - 5 = 3( y - 5 )
x- 5 = 3y - 15
x - 3y - 5 + 15 = 0
x - 3y + 10 = 0 ------(1)

x + 10 = 2( y + 10 )
x + 10 - 2y - 10 = 0
x - 2y = 0 -------(2)

(1) - (2)

x - 3y + 10 = 0
-( x - 2y ) = 0

- y + 10 = 0
y = 10

Keeping value of y in 2nd eqn

x - 2y = 0
x - 2 × 10 = 0
x = 20

Hope it helps☺!✌

Answer 2

Let the present age of Amit be x.
Let the present age of Armaan be y.

Given that 5 years ago, Amit was three times as old as Armaan.
x - 5 = 3(y-5)
x - 5 = 3y - 15
x = 3y - 10---------(i)

Given that ten years later, Amit would be twice as old as Armaan.
x + 10 = 2(y + 10)
x + 10 = 2y + 20
x = 2y + 10---------(ii)

On solving (i) and (ii), we get
3y = 2y + 20
3y - 2y = 20
y = 20----------(iii)

Substituting (iii) in (i), we get
x = 3y - 10
= 3(20) - 10
= 60 - 10
= 50.

Therefore, the present age of Amit is 50, &
the present age of Armaan is 20.

$hope \: it \: helps \: you. \\ .dev.$