Bryan, Simon and Ian had some beads. Simon had 20% more beads than Bryan. Simon had ³₅ of Ian's. After Bryan gave 45 beads to Simon, he had ¹₃ of what Simon had. How many more beads did Ian have than Simon in the end?

Bryan	Simon	Ian
5x1	6x1
	3x2	5x2
5	6	10

	Ian	Bryan	Simon	Total beads of  Bryan and Simon
Before	10x4 = 40 u	5x4 = 20 u	6x4 = 24 u	11x4 = 44 u
Change		- 45	+ 45
After	40 u	1x11 = 11 u	3x11 = 33 u	4x11 = 44 u

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

120% = ¹²⁰₁₀₀ = ⁶₅

Bryan : Simon = 5 : 6

The number of beads that Simon had at first is repeated.  Make the number of beads that Simon had at first the same.  LCM of 6 and 3 is 6.

When Bryan gave 45 beads to Simon, the total number of beads that Simon and Bryan had at first and in the end remains the same.  Make the total number of beads that Simon and Bryan had the same.  LCM of 11 and 4 is 44.

Number of beads that Bryan gave to Simon
= 20 u - 11 u
= 9 u

9 u = 45

1 u = 45 ÷ 9 = 5

Number of beads that Ian had more than Simon in the end
= 40 u - 33 u
= 7 u
= 7 x 5
= 35

Answer(s): 35