Ahmad and Tom shared some stamps in the ratio of 5 : 8. After both each gave away 119 stamps to their sister, the ratio of the number of stamps Ahmad had to the total number of stamps left was 1 : 6. How many stamps did the two boys have at first?

	Ahmad	Tom	Difference
Before	5x4 = 20 u	8x4 = 32 u	3x4 = 12 u
Change	- 119	- 119
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of stamps that Ahmad and Tom each gave to their sister is the same.

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

Number of stamps that Ahmad gave to their sister
= 20 u - 3 u
= 17 u

17 u = 119

1 u = 119 ÷ 17 = 7

Number of stamps that the two boys had at first
= 20 u + 32 u
= 52 u
= 52 x 7
= 364

Answer(s): 364