Archie is 30 years older than his cousin. 3 years from now, his cousin will be ¹₂ of his age while his nephew will be ²₅ of his cousin. Express his nephew’s present age as a fraction of Archie's present age. Leave your answer in its simplest form.

	Archie	Archie's cousin	Archie's nephew	Difference between Archie and Archie's cousin
Before	10 u - 3	5 u - 3	2 u - 3	30
Change	+ 3	+ 3	+ 3
After	2x5	1x5
		5x1	2x1
Comparing Archie, his cousin and his nephew in the end	10 u	5 u	2 u	5 u

The repeated identity is the age of Archie's cousin. LCM of 1 and 5 is 5.

The difference in age between Archie and Archie's cousin remains unchanged.

Difference in age between Archie and Archie's cousin
= 10 u - 5 u 
= 5 u 

5 u = 30

1 u = 30 ÷ 5 = 6

His nephew's present age 
= 2 u - 3
= 2 x 6 - 3
= 12 - 3
= 9

Archie's present age
= 10 u - 3
= 10 x 6 - 3
= 60 - 3
= 57

His nephew's present age as a fraction of Archie's present age
= ⁹₅₇
= ³₁₉

Answer(s): ³₁₉