Jamie had 25% more pens than John. Aria had 50% fewer pens than Jamie. Jamie and John gave Aria some pens in the ratio of 1 : 3. As a result, Aria had 60% more pens than before. Given that John had 27 less pens than Aria in the end, how many pens did John give to Aria?

Jamie	John	Aria
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Jamie : John = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Jamie : Aria = 2 : 1

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

	Jamie	John	Aria
Before	10x4 =  40 u	8x4 = 32 u	5x4 = 20 u
Change			+ 3x4 = + 12 u
Comparing the changes in the number of pens	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	37 u	23 u	8x4 = 32 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of pens that Jamie and John gave to Aria is repeated.  Make the total number of pens that Jamie and John gave to Aria the same.  LCM of 4 and 3 is 12.

Number of pens that John had less than Aria 
= 32 u - 23 u
= 9 u

9 u = 27

1 u = 27 ÷ 9 = 3

Number of pens that John gave to Aria
= 9 u
= 9 x 3
= 27

Answer(s): 27