Julian, Simon and Japheth have some cards. The ratios of their cards are as follows:

Julian : (Julian + Simon + Japheth) = 1 : 4
Simon : (Julian + Japheth) = 1 : 5

Japheth has 30 cards more than Simon. In the end, Japheth gives away all he has to Simon and Julian so that both Simon and Julian end up with the same number of cards, how many cards has Simon received from Japheth?

Simon	Japheth	Julian	Total
3x3		1x3	4x3
1x2	5x2		6x2
2 u	7 u	3 u	12 u

The total number of cards is repeated.  Make the total number of cards the same.  LCM of 4 and 6 is 12.

Number of cards that Japheth has more than Simon
= 7 u - 2 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

	Simon	Japheth	Julian
Before	2 u	7 u	3 u
Change	+ 4 u	- 7 u	+ 3 u
After	6 u	0 u	6 u

Number of cards that Simon has received from Japheth
= 6 u - 2 u 
= 4 u
= 4 x 6
= 24

Answer(s): 24