Liam, Ahmad and Vincent had some beads. Ahmad had 80% more beads than Liam. Ahmad had ²₅ of Vincent's. After Liam gave 33 beads to Ahmad, he had ¹₃ of what Ahmad had. How many more beads did Vincent have than Ahmad in the end?

Liam	Ahmad	Vincent
5x2	9x2
	2x9	5x9
10	18	45

	Vincent	Liam	Ahmad	Total beads of  Liam and Ahmad
Before	45x1 = 45 u	10x1 = 10 u	18x1 = 18 u	28x1 = 28 u
Change		- 33	+ 33
After	45 u	1x7 = 7 u	3x7 = 21 u	4x7 = 28 u

Number of beads that Ahmad had more than Liam at first in percent
= 100%+ 80%
= 180%

180% = ¹⁸⁰₁₀₀ = ⁹₅

Liam : Ahmad = 5 : 9

The number of beads that Ahmad had at first is repeated.  Make the number of beads that Ahmad had at first the same.  LCM of 9 and 2 is 18.

When Liam gave 33 beads to Ahmad, the total number of beads that Ahmad and Liam had at first and in the end remains the same.  Make the total number of beads that Ahmad and Liam had the same.  LCM of 28 and 4 is 28.

Number of beads that Liam gave to Ahmad
= 10 u - 7 u
= 3 u

3 u = 33

1 u = 33 ÷ 3 = 11

Number of beads that Vincent had more than Ahmad in the end
= 45 u - 21 u
= 24 u
= 24 x 11
= 264

Answer(s): 264