Question

Five years ago, Lucky was three times as old as lovely. 10 years later, lucky would be twice as 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.

Answer 2

Hey!!
Here is the answer..

Let the present age of lucky be 'x' years.
Let the present age of lovely be 'y' years.

According to the first condition,
Lucky's age 5 years ago = x - 5 years.
Lovely's age 5 years ago = y - 5 years.

According to the next condition,
x - 5 = 3 ( y - 5 )
x - 5 = 3y - 15
x - 3y - 5 +15 = 0
$\text{x - 3y - 10 = 0... Equation 1.}$

Now,
After ten years ,
Lucky's age = x + 10
Lovely's age = y + 10

According to next condition,
x + 10 = 2 ( y + 10 )
x + 10 = 2y + 20
x - 2y + 10 - 20 = 0
$\text{x - 2y -10 = 0.... Equation 2.}$


Now ,
From Equation 1,
x - 3y - 10 = 0
Therefore,
x - 3y = 10
$\text{x= 10 + 3y... Equation 3.}$


Substituting Equation 3 in Equation 2,

-10 + 3y - 2y - 10 = 0
-10 + y - 10 = 0
-20 + y = 0
$\text{y = 20 years }$

Hence the age of Lovely is 20 years.

Now,
Substituting the value of 'y' in Equation 1.

x - 3y - 10 = 0
x- 3 × 20 - 10 = 0
x - 60 + 10 = 0
x - 50 = 0
$\text{x = 50 years.}$


Hence the age of Lucky is 50 years.
$\bold{x = 50 years }\\ \bold{y = 20 years}$

I hope my answer helped!!

Thanks!!

#BeBrainly!!