Howard is 30 years older than his niece. 3 years from now, his niece will be ¹₃ of his age while his nephew will be ²₅ of his niece. Express his nephew’s present age as a fraction of Howard's present age. Leave your answer in its simplest form.

	Howard	Howard's niece	Howard's nephew	Difference between Howard and Howard's niece
Before	15 u - 3	5 u - 3	2 u - 3	30
Change	+ 3	+ 3	+ 3
After	3x5	1x5
		5x1	2x1
Comparing Howard, his niece and his nephew in the end	15 u	5 u	2 u	10 u

The repeated identity is the age of Howard's niece. LCM of 1 and 5 is 5.

The difference in age between Howard and Howard's niece remains unchanged.

Difference in age between Howard and Howard's niece
= 15 u - 5 u 
= 10 u 

10 u = 30

1 u = 30 ÷ 10 = 3

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

Howard's present age
= 15 u - 3
= 15 x 3 - 3
= 45 - 3
= 42

His nephew's present age as a fraction of Howard's present age
= ³₄₂
= ¹₁₄

Answer(s): ¹₁₄