Question

Five years ago lucky was three times as old as lovely. Ten years later lucky would be twice as much old as lovely. How old are they now?

Answer 1

Let the present age of lucky be x yrs
And the present age of lovely be y yrs
According to question
Five years ago
Lucky's age = x-5
Lovely's age = y-5
x-5 = 3(y-5)
x-5=3y-15
x-3y+10=0 - - - - (1)
Ten years later
Lucky's age = x+10
Lovely's age =y+10
(x+10) = 2(y+10)
x+10 = 2y+20
x-2y-10 = 0 - - - - - - (2)

x-3y+10=0
x-3y=-10
x = - 10+3y
Substituting the value of x in eq 2
-10+3y-2y-10 = 0
-10+y-10=0
-10+y=10
y=10+10
y=20

X= - 10+3y
= - 10+3*20
= - 10+60
= 50

The present age of Lucky is 50 years
And the present age of Lovely is 20 years.

HOPE IT WILL HELP YOU!!!

Answer 2

let x be lucky's age and y be lovely's age presently.

so five years ago,

                x - 5 = 3 (y -5)

                x - 5 = 3y -15

                x = 3y - 10

ten years later,

               x + 10 = 2 ( y + 10)

               x + 10 = 2y + 20

               x  = 2y + 10

since you see that x = 3y - 10 and x = 2y + 10, then,

             3y - 10 = 2y + 10

             3y = 2y + 20

              y = 20

sub this value into x = 2y + 10

             x = 2 (20) + 10

             x = 50

so, Lucky is 50 and Lovely is 20 now.