Answer:
Charlotte's age = 30 years
Olivia's age = 50 years
Step-by-step explanation:
Present ages of Charlotte & Olivia = 6:10.
Then, their present ages are:
Charlotte = 6x
Olivia = 10x
Now, in 10 years, their ratio = 4:6
Then,
Ratio of Charlotte's & Olivia's present age + 10 years each = Ratio of their ages in 10 years
[tex]\frac{6x + 10}{10x + 10} = \frac{4}{6} \\6(6x + 10) = 4 (10x + 10) \: \: \: \: [\mathrm{cross\: multiplication}]\\36x + 60 = 40x + 40\\36x - 40x = 40 - 60\\4x = 20\\\boxed{\bf\:x = 5}[/tex]
So,
Charlotte's present age [tex]= 6x = 6(5) = {\boxed{\bf\:30 \:years}[/tex]
Olivia's present age = [tex]10x = 10(5) = \boxed{\bf\:50 \: years}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
