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?

Answer 1

Let present age of Amit = x

present age of armaan = y

5 years ago ,

(x-5) = 3(y-5)

x-5 = 3y-15

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

10 yeras later,

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

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


from solving equation (1) & (2)


x = 50 years

y = 20 years


so, present age of Amit = x = 50 years

present age of armaan = y = 20 years




Hope it helps

Answer 2

$hi...$
Let the Amit's age be x and age of Armaan be y.

Five years ago ,
Amit's age : x - 5
Armaan's age : y - 5

By the condition,
x - 5 = 3(y - 5)
x - 5 = 3y - 15
x - 3y = -15 + 5
x - 3y = -10 .........................(1)

10 years later ......

Amit's age : x + 10
Armaan's age : y + 10

By the 2nd condition ,

x + 10 = 2(y + 10)
x + 10 = 2y +20
x - 2y = 20 - 10
x - 2y = 10 .........................(2)

[Subtracting equation no. (2) from (1)]

x - 3y = -10
x - 2y = 10
_________
-y = -20

y = 20

Substitute y = 20 in equation no. (2)
x - 2y = 10
x - 2(20) = 10
x - 40 = 10
x = 10 + 40
x = 50

$solution...$
$x = 50 \: \: \: . \: \: \: y = 20$
Thus ,
The Amit is 50 yrs old and Armaan is age is 20yrs old.

$hope \: this \: helps...$