At first, Dylan, Esther and Simon had some lollipops in the ratio 5 : 3 : 4 respectively. Dylan had 405 lollipops. Then he gave all his lollipops to Esther and Simon. After receiving the lollipops from Dylan, Esther and Simon had the same number of lollipops. How many lollipops did Esther receive from Dylan?

	Dylan	Esther	Simon	Total
Before	5x1 = 5 u	3x1 = 3 u	4x1 = 4 u	12x1 = 12 u
Change	- 5 u	+ 5 u
After	0	1x6 = 6 u	1x6 = 6 u	2x6 = 12 u

The total number of lollipops remains unchanged. Make the total number of lollipops the same.  LCM of 2 and 12 is 12.

Total number of lollipops = 12 u

Number of lollipops that Esther had in the end 
= 12 u ÷ 2
= 6 u

Number of lollipops that Dylan had at first = 5 u 

5 u = 405

1 u = 405 ÷ 5 = 81

Number of lollipops that Esther received from Dylan
= 6 u - 3 u
= 3 u
= 3 x 81
= 243

Answer(s): 243