Zeph, Harry and Ethan had some beads. Harry had 20% more beads than Zeph. Harry had ²₅ of Ethan's. After Zeph gave 44 beads to Harry, he had ¹₂ of what Harry had. How many more beads did Ethan have than Harry in the end?

Zeph	Harry	Ethan
5x1	6x1
	2x3	5x3
5	6	15

	Ethan	Zeph	Harry	Total beads of  Zeph and Harry
Before	15x3 = 45 u	5x3 = 15 u	6x3 = 18 u	11x3 = 33 u
Change		- 44	+ 44
After	45 u	1x11 = 11 u	2x11 = 22 u	3x11 = 33 u

Number of beads that Harry had more than Zeph at first in percent
= 100%+ 20%
= 120%

120% = ¹²⁰₁₀₀ = ⁶₅

Zeph : Harry = 5 : 6

The number of beads that Harry had at first is repeated.  Make the number of beads that Harry had at first the same.  LCM of 6 and 2 is 6.

When Zeph gave 44 beads to Harry, the total number of beads that Harry and Zeph had at first and in the end remains the same.  Make the total number of beads that Harry and Zeph had the same.  LCM of 11 and 3 is 33.

Number of beads that Zeph gave to Harry
= 15 u - 11 u
= 4 u

4 u = 44

1 u = 44 ÷ 4 = 11

Number of beads that Ethan had more than Harry in the end
= 45 u - 22 u
= 23 u
= 23 x 11
= 253

Answer(s): 253