Question

5 years ago, Amit was 3 times as old as Armaan. 10 years later Amit would be twice as old as Armaan. how old they now?​

Answer 1

5 years ago Amit was 3 times as old as Armaan

Let Armaan age 5 years ago=x years

Then Amit age 5 years ago=3x years

Present age of Armaan=(x+5) years

Present age of Amit=(3x+5) years

10 years later.

Age of Armaan will be=(x+5+10)=(x+15) years

Age of Amit will be=(3x+5+10)=(3x+15) years

Now Amit is also 2 times as old as Armaan

Means

Armaan age after 10 years=2×amit age after 10 years

3x+15=2(x+15)

3x+15=2x+30

3x-2x=30-15

x=15

Present age of Armaan=(x+5)=15+5=20 years

Present age of Amit=(3x+5)=3×15+5=50 years

$\boxed{\mathbf{\huge{Armaan=20\:years}}}$

$\boxed{\mathbf{\huge{Amit=50\:years}}}$

Answer 2

Solution:

let Amit be x years old and Armaan be y years old.

5 years ago,

Amit was x-5 years and Armaan was y-5 years

accordingly,

x-5=3(y-5)

x-5=3y-15

x-3y= -10....(1)

also,

after 10 years,

Amit will be x+ 10 years old and Armaan would be y+10 years

accordingly,

x+10= 2y+20

x-2y= 10.....(2)

now,

subtracting (2) from(1)

x-3y= -10

- x+ 2y= -10

-y= -20

y = Armaan's age= 20 years

now substituting value of y in (1)

x-3y= -10

x- 3(20) =-10

x-60=-10

x= 60-10

x= 50

therefore,

Amit is 50 years old

hope this helps!! ☺❤✌