Question

Monica is one-third as olf as her sister. six years hence she will be one-half as old as her sister find their present age

Answer 1

Direct method:
sister ---- x
Monica --- (1/3)x or x/3

6 years from now:
age of sister = x+6
Monica's age = x/3 + 6

x/3 + 6 = (1/2)(x+6)
multiply each term by 6, the LCD
2x + 36 = 3(x+6)
2x+36 = 3x + 18
18 = x

The sister is 18, and Monica is 6

or

sometimes fractions can be avoided by rephrasing the conditions:
if Monica is 1/3 her sister's age, then the sister is 3 times as old as Monica
let Monica's age be y
then sister's age is 3y

in 6 years, Monica will be y+6 and the sister 3y+6
At that time, Monica is half as old as the sister,
or
the sister is twice as old as Monica
3y+6 = 2(y+6)
3y + 6 = 2y+12
y = 6 , ---> 3y = 18

So Monica is 6, the sister is 18

Answer 2

Monica is one-third as old as her sister. Six years hence, she will be one-half as old as her sister. Find the present age of monica