Question

The ages of Charlotte and Olivia are in the ratio 6:10. After 10 years, their ratio will become 4:6. Find their ages.

Answer 1

Charlotte's age = 30 years

Olivia's age = 50 years

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

`(6x + 10)/(10x + 10) = (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}`

So,

Charlotte's present age
`= 6x = 6(5) = {\boxed{\bf\:30 \:years}`

Olivia's present age =
`10x = 10(5) = \boxed{\bf\:50 \: years}`

`\rule{150pt}{2pt}`