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

let the amit age be x and armann be y
five years ago
amit=x-5
armann=y-5
a.t.q
x-5=3(y-5)
x-5=3y-15
x-3y +10=0

ten years later
amit=x+10
armann=y+10
x+10=2(y+10)
x+10=2y+20
x-2y=10
on putting x=3y-10
we gat
3y-10-2y=10
y=20 years
x=50 years

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 ------ (1)

ATP

ten years later Amit would be twice as old as Armaan.

x + 10 = 2(y + 10)

x + 10 = 2y + 20

x = 2y + 10  ---- (2)

On solving (1) and (2), we get

3y - 10 = 2y + 10

3y = 2y + 20

3y - 2y = 20

y = 20  ---- (3)

Substitute (3) in (1), we get

x = 3y - 10

= 3(20) - 10  = 50.

∴ the present age of Amit is 50.     ANS

 the present age of armaan is 20.   ANS