Daniel and Archie shared some stamps in the ratio of 4 : 7. After both each gave away 78 stamps to their cousin, the ratio of the number of stamps Daniel had to the total number of stamps left was 1 : 6. How many stamps did the two boys have in the end?

	Daniel	Archie	Difference
Before	4x4 = 16 u	7x4 = 28 u	3x4 = 12 u
Change	- 78	- 78
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of stamps that Daniel and Archie each gave to their cousin is the same.

The difference in the number of stamps at first and in the end between Daniel and Archie remains unchanged.  Make the difference in the number of stamps the same.  LCM of 3 and 4 is 12.

Number of stamps that Daniel gave to their cousin
= 16 u - 3 u
= 13 u

13 u = 78

1 u = 78 ÷ 13 = 6

Number of stamps that the two boys had in the end
= 3 u + 15 u
= 18 u
= 18 x 6
= 108

Answer(s): 108