Rael had 50% more pencils than Sophia. Roshel had 20% fewer pencils than Rael. Rael and Sophia gave Roshel some pencils in the ratio of 4 : 5. As a result, Roshel had 25% more pencils than before. Given that Sophia had 240 less pencils than Roshel in the end, how many pencils did Sophia give to Roshel?

Rael	Sophia	Roshel
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Rael : Sophia = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Rael : Roshel = 5 : 4

The number of pencils that Rael had at first is repeated. Make the number of pencils that Rael had at first the same.  LCM of 3 and 5 is 15.

	Rael	Sophia	Roshel
Before	15x3 =  45 u	10x3 = 30 u	12x3 = 36 u
Change			+ 3x3 = + 9 u
Comparing the changes in the number of pencils	- 4x1 = - 4 u	- 5x1 = - 5 u	+ 9x1 = + 9 u
After	41 u	25 u	15x3 = 45 u

25% x 12 
= ²⁵₁₀₀ x 12 
= 3 

The total number of pencils that Rael and Sophia gave to Roshel is repeated.  Make the total number of pencils that Rael and Sophia gave to Roshel the same.  LCM of 9 and 3 is 9.

Number of pencils that Sophia had less than Roshel 
= 45 u - 25 u
= 20 u

20 u = 240

1 u = 240 ÷ 20 = 12

Number of pencils that Sophia gave to Roshel
= 5 u
= 5 x 12
= 60

Answer(s): 60