In February, Shiyun and Oscar had pens in the ratio 2 : 1. In March, each of them gave away the same number of pens. Shiyun then had five times as many pens as Oscar.

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

	Shiyun	Oscar	Difference
Before	2x4 = 8 u	1x4 = 4 u	1x4 = 4 u
Change	- 3 u	- 3 u
After	5x1 = 5 u	1x1 = 1 u	4x1 = 4 u

(a)
Since Shiyun and Oscar gave away the same number of pens, the difference in the number of pens between Shiyun and Oscar at first and in the end remains the same.

Make the difference in the number of pens at first and in the end the same. LCM of 1 and 4 is 4.

Oscar's pens in February : Oscar's pens in March
4 : 1

(b)
Total number of pens in February
= 8 u + 4 u
= 12 u

Total number of pens in March
= 5 u + 1 u
= 6 u

Total pens in February : Total pens in March
12 : 6 _(÷6)
2 : 1 

Answer(s): (a) 4 : 1; (b) 2 : 1