Simon, Paul and Rael had some beads. Paul had 20% less beads than Simon. Paul had ²₇ of Rael's. After Simon gave 84 beads to Paul, he had ¹₅ of what Paul had. How many more beads did Rael have than Simon in the end?

Simon	Paul	Rael
5x1	4x1
	2x2	7x2
5	4	14

	Rael	Simon	Paul	Total beads of  Simon and Paul
Before	14x2 = 28 u	5x2 = 10 u	4x2 = 8 u	9x2 = 18 u
Change		- 84	+ 84
After	28 u	1x3 = 3 u	5x3 = 15 u	6x3 = 18 u

Number of beads that Paul had less than Simon at first in percent
= 100% - 20%
= 80%

80% = ⁸⁰₁₀₀ = ⁴₅

Simon : Paul = 5 : 4

The number of beads that Paul had at first is repeated.  Make the number of beads that Paul had at first the same.  LCM of 4 and 2 is 4.

When Simon gave 84 beads to Paul, the total number of beads that Paul and Simon had at first and in the end remains the same.  Make the total number of beads that Paul and Simon had the same.  LCM of 9 and 6 is 18.

Number of beads that Simon gave to Paul
= 10 u - 3 u
= 7 u

7 u = 84

1 u = 84 ÷ 7 = 12

Number of beads that Rael had more than Simon in the end
= 28 u - 3 u
= 25 u
= 25 x 12
= 300

Answer(s): 300