Oliver, Daniel and Zane had some beads. Daniel had 40% more beads than Oliver. Daniel had ⁴₇ of Zane's. After Oliver gave 96 beads to Daniel, he had ¹₃ of what Daniel had. How many more beads did Zane have than Daniel in the end?

Oliver	Daniel	Zane
5x4	7x4
	4x7	7x7
20	28	49

	Zane	Oliver	Daniel	Total beads of  Oliver and Daniel
Before	49x1 = 49 u	20x1 = 20 u	28x1 = 28 u	48x1 = 48 u
Change		- 96	+ 96
After	49 u	1x12 = 12 u	3x12 = 36 u	4x12 = 48 u

Number of beads that Daniel had more than Oliver at first in percent
= 100%+ 40%
= 140%

140% = ¹⁴⁰₁₀₀ = ⁷₅

Oliver : Daniel = 5 : 7

The number of beads that Daniel had at first is repeated.  Make the number of beads that Daniel had at first the same.  LCM of 7 and 4 is 28.

When Oliver gave 96 beads to Daniel, the total number of beads that Daniel and Oliver had at first and in the end remains the same.  Make the total number of beads that Daniel and Oliver had the same.  LCM of 48 and 4 is 48.

Number of beads that Oliver gave to Daniel
= 20 u - 12 u
= 8 u

8 u = 96

1 u = 96 ÷ 8 = 12

Number of beads that Zane had more than Daniel in the end
= 49 u - 36 u
= 13 u
= 13 x 12
= 156

Answer(s): 156