Luis is 20 years older than his daughter. 6 years from now, his daughter will be ¹₂ of his age while his niece will be ³₅ of his daughter. Express his niece’s present age as a fraction of Luis's present age. Leave your answer in its simplest form.

	Luis	Luis's daughter	Luis's niece	Difference between Luis and Luis's daughter
Before	10 u - 6	5 u - 6	3 u - 6	20
Change	+ 6	+ 6	+ 6
After	2x5	1x5
		5x1	3x1
Comparing Luis, his daughter and his niece in the end	10 u	5 u	3 u	5 u

The repeated identity is the age of Luis's daughter. LCM of 1 and 5 is 5.

The difference in age between Luis and Luis's daughter remains unchanged.

Difference in age between Luis and Luis's daughter
= 10 u - 5 u 
= 5 u 

5 u = 20

1 u = 20 ÷ 5 = 4

His niece's present age 
= 3 u - 6
= 3 x 4 - 6
= 12 - 6
= 6

Luis's present age
= 10 u - 6
= 10 x 4 - 6
= 40 - 6
= 34

His niece's present age as a fraction of Luis's present age
= ⁶₃₄
= ³₁₇

Answer(s): ³₁₇