At first, Xavier, Olivia and Ivan had some sweets in the ratio 6 : 4 : 5 respectively. Xavier had 360 sweets. Then he gave all his sweets to Olivia and Ivan. After receiving the sweets from Xavier, Olivia and Ivan had the same number of sweets. How many sweets did Olivia receive from Xavier?

	Xavier	Olivia	Ivan	Total
Before	6x2 = 12 u	4x2 = 8 u	5x2 = 10 u	15x2 = 30 u
Change	- 6 u	+ 6 u
After	0	1x15 = 15 u	1x15 = 15 u	2x15 = 30 u

The total number of sweets remains unchanged. Make the total number of sweets the same.  LCM of 2 and 15 is 30.

Total number of sweets = 30 u

Number of sweets that Olivia had in the end 
= 30 u ÷ 2
= 15 u

Number of sweets that Xavier had at first = 6 u 

6 u = 360

1 u = 360 ÷ 6 = 60

Number of sweets that Olivia received from Xavier
= 15 u - 8 u
= 7 u
= 7 x 60
= 420

Answer(s): 420