Question

My cousin, Ravi, is three times younger than me, but two and a half times older than my daughter. If our total ages are 66, how old is my cousin?

Answer 1

Writing `r` for Ravi's age, `m` for "my" age and `d` for "my daughter's" age, we are given:

`r = m/3`

`r = 2.5d = (5/2)d`

`r+m+d = 66`

and we are trying to determine `r`.

Multiplying the first equation by `3` on both sides, we find `m=3r`.

Multiplying the second equation by `2/5` on both sides, we find `d = (2/5)r`

Substituting for `m` and `d` in the third equation, we find

`66 = r+m+d = r + 3r + (2/5)r`

`= (1+3+(2/5))r`

`= (5/5 + 15/5+2/5)r`

`= ((5+15+2)/5)r`

`= (22/5)r`

Multiplying both ends of this equation by (5/22) we get:

`r = 66xx(5/22) = (66xx5)/22 = (22xx3xx5)/22 = 15`

So Ravi is 15 years old. "my" age is 45 and "my daughter's" age is 6.