Question

five years ago juhi was three times as old as amreen. 10 years later, juhi would be twice as old as amreen.how old are they.​

Answer 1

Solution:-

Let the age of Juhi be "x" years and that of Amreen be "y" years.

5 Years Ago,

Age of Juhi = ( x - 5) yrs

Age of Amreen = ( y - 5) yrs

Condition I,

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

=) x - 5 = 3y - 15

=) x = 3y - 15 + 5

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

10 Years Later,

Age of Juhi = ( x + 10) yrs

Age of Amreen = ( y + 10) yrs

Condition II,

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

=) 3y - 10 + 10 = 2y + 20

=) 3y - 2y = 20

=) y = 20

Substituting [ y = 20 ] in eq(1).

=) x = 3y - 10

=) x = 60 - 10

=) x = 50 yrs.

Hence,

Age of Juhi = x = 50 yrs.

Age of Amreen = y = 20 yrs.

Answer 2

Solution :-

Let the present ages of Juhi and Amreen be "x" and "y".

5 Years ago ;

Age of Juhi = (x - 5)

Age of Amreen = (y - 5)

According To Question :-

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

= x - 5 = 3y - 15

= x = 3y - 15 + 5

= x = 3y - 10

= x - 3y = -10

10 Years later ;

Age of Juhi = (x + 10)

Age of Amreen = (y + 10)

According To Question :-

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

= x + 10 = 2y + 20

= x - 2y = 10

Solve (2) & (1) by Elimination method :-

x - 3y = -10

x - 2y = 10

Multiply the 2nd equation be (-).

x - 3y = -10

-x + 2y = -10

____________

-y = -20

y = 20

Substitute (y = 20) in equation (1) ;

x - 3y = -10

x - 3 (20) = -10

x - 60 = -10

x = -10 + 60

x = 50

So,

The present age of Juhi = 50 Years.

Present age of Amreen = 20 years.