Question

When a girl will be just as old as her
mother today, the addition of their ages
will be 126; when the girl's mother was
as old as her daughter is today, the addi-
tion of their ages then was 38. Find their
present ages.​

Answer 1

Answer:

[Mother 's new age] + [Girl 's new age] =126

[y+(y−x)]+[(x+(y−x))]=126

⇒2y−x+y=126

∴3y−x=126        ..........(1)

[Mother 's previous age] + [girl's previous age]=38

[y−(y−x)]+[x−(y−x)]=38

⇒x+x−y+x=38

⇒3x−y=38

∴y=3x−38          .........(2)

Now sub eqn(2) into equation(1)

⇒3(3x−38)−x=126

⇒9x−114−x=126

⇒8x=240

∴x=30  

Now y=3x−38

⇒y=3(30)−38

∴y=52

The Girl is 30 years old, and the Mother 52 years old.

Step-by-step explanation: