Christian had 25% more pencils than Oliver. Benjamin had 50% fewer pencils than Christian. Christian and Oliver gave Benjamin some pencils in the ratio of 4 : 5. As a result, Benjamin had 60% more pencils than before. Given that Oliver had 35 less pencils than Benjamin in the end, how many pencils did Oliver give to Benjamin?

Christian	Oliver	Benjamin
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Christian : Oliver = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Christian : Benjamin = 2 : 1

The number of pencils that Christian had at first is repeated. Make the number of pencils that Christian had at first the same.  LCM of 5 and 2 is 10.

	Christian	Oliver	Benjamin
Before	10x3 =  30 u	8x3 = 24 u	5x3 = 15 u
Change			+ 3x3 = + 9 u
Comparing the changes in the number of pencils	- 4x1 = - 4 u	- 5x1 = - 5 u	+ 9x1 = + 9 u
After	26 u	19 u	8x3 = 24 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of pencils that Christian and Oliver gave to Benjamin is repeated.  Make the total number of pencils that Christian and Oliver gave to Benjamin the same.  LCM of 9 and 3 is 9.

Number of pencils that Oliver had less than Benjamin 
= 24 u - 19 u
= 5 u

5 u = 35

1 u = 35 ÷ 5 = 7

Number of pencils that Oliver gave to Benjamin
= 5 u
= 5 x 7
= 35

Answer(s): 35