Claire bought 25% more pens than Rachel. Joseph bought 20% fewer pens than Claire. Claire and Rachel gave Joseph some pens in the ratio 3 : 2. As a result, Joseph had twice as much pens as before. Given that Rachel had 24 more pens than Claire in the end, how much pens did Joseph receive?

	Claire	Rachel	Joseph
	5x5	4x5
	5x5		4x5
Before	25 u	20 u	20 u
Change			+ (2 x 20 u) = + 40 u
	- 3x8 = - 24 u	- 2x8 = - 16 u	+ 5x8 =  + 40 u
After	1 u	4 u	60 u

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

The number of pens that Claire had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of pens that Joseph had is the repeated identity when Claire and Rachel gave to Joseph.
LCM of 40 and 5 = 40

Number of pens that Rachel had more than Claire in the end
= 4 u - 1 u
= 3 u

3 u = 24
1 u = 24 ÷ 3 = 8

Number of pens that Joseph received
= 24 u + 16 u
= 40 u
= 40 x 8
= 320

Answer(s): 320