Vaidev and Ahmad shared some beads in the ratio of 5 : 7. After both each gave away 30 beads to their cousin, the ratio of the number of beads Vaidev had to the total number of beads left was 1 : 3. How many beads did the two boys have in the end?

	Vaidev	Ahmad	Difference
Before	5x1 = 5 u	7x1 = 7 u	2x1 = 2 u
Change	- 30	- 30
After	1x2 = 2 u	2x2 = 4 u	1x2 = 2 u

Number of beads that Vaidev and Ahmad each gave to their cousin is the same.

The difference in the number of beads at first and in the end between Vaidev and Ahmad remains unchanged.  Make the difference in the number of beads the same.  LCM of 2 and 1 is 2.

Number of beads that Vaidev gave to their cousin
= 5 u - 2 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Number of beads that the two boys had in the end
= 2 u + 4 u
= 6 u
= 6 x 10
= 60

Answer(s): 60