In February, Xandra and Ahmad had beads in the ratio 11 : 6. In March, each of them gave away the same number of beads. Xandra then had thrice as many beads as Ahmad.

1. Find the ratio of the number of beads Ahmad had in February to the number of beads he had in March.
2. Find the ratio of the total number of beads both had in February to the total number of beads both had in March.

	Xandra	Ahmad	Difference
Before	11x2 = 22 u	6x2 = 12 u	5x2 = 10 u
Change	- 7 u	- 7 u
After	3x5 = 15 u	1x5 = 5 u	2x5 = 10 u

(a)
Since Xandra and Ahmad gave away the same number of beads, the difference in the number of beads between Xandra and Ahmad at first and in the end remains the same.

Make the difference in the number of beads at first and in the end the same. LCM of 5 and 2 is 10.

Ahmad's beads in February : Ahmad's beads in March
12 : 5

(b)
Total number of beads in February
= 22 u + 12 u
= 34 u

Total number of beads in March
= 15 u + 5 u
= 20 u

Total beads in February : Total beads in March
34 : 20 _(÷2)
17 : 10 

Answer(s): (a) 12 : 5; (b) 17 : 10