In February, Gem and Riordan had pens in the ratio 8 : 5. In March, each of them gave away the same number of pens. Gem then had five times as many pens as Riordan.

1. Find the ratio of the number of pens Riordan 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.

	Gem	Riordan	Difference
Before	8x4 = 32 u	5x4 = 20 u	3x4 = 12 u
Change	- 17 u	- 17 u
After	5x3 = 15 u	1x3 = 3 u	4x3 = 12 u

(a)
Since Gem and Riordan gave away the same number of pens, the difference in the number of pens between Gem and Riordan 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 3 and 4 is 12.

Riordan's pens in February : Riordan's pens in March
20 : 3

(b)
Total number of pens in February
= 32 u + 20 u
= 52 u

Total number of pens in March
= 15 u + 3 u
= 18 u

Total pens in February : Total pens in March
52 : 18 _(÷2)
26 : 9 

Answer(s): (a) 20 : 3; (b) 26 : 9