The sum of the present ages of Mark and his mother is 60 years. In 6 years she will be twice as old as he will be. Find their present ages.

In 6 years, 12 years will be added to the total of their ages, so it will be 72. Since this is the total of Mark's age and twice Mark's age, his age at that time will be 72/3 = 24. His mother will be 48 at that time.

Now, they are 6 years younger than that, so they are 18 and 42.

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akiran007 akiran007 · Answer 2 · 2021-10-19T03:53:47+02:00

This question can be solved using 2 variables x and y.

Putting the variables in the equation according to the conditions given would give the value of the variable.

In 6 years time the age of Mark will be 18+6=24 years and his mother will be 42+6=48 years which will be twice of 24.

Let the present age of Mark be x and his mother be y.

Then according to the given conditions.

x+y= 60 ---- equation 1

y+6= 2(x+6)

y+6= 2x+12

y-6= 2x------equation2

From equation 1 the value of y is found to be

y= 60-x------ equation3

Putting this value of y from equation 3 in equation 2

y-6-2x

60-x -6 = 2x

54= 2x+x

54=3x

x= 54/3= 18

The present age of Mark is 18 years.

Putting x= 18 in equation 1

18+y=60

y= 60-18= 42

His mother is 42 years old.

In 6 years time the age of Mark will be 18+6=24 years and his mother will be 42+6=48 years which will be twice of 24.

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