There were 205 blue, grey and purple files in a box. 15 purple files were removed from the box and the ratio of the number of blue files to the number of grey files to the number of purple files became 5 : 2 : 3. Then some white files were added and the ratio of the number of purple files to the number of white files was 3 : 4.

1. What was the ratio of the number of blue files to the number of grey files to the number of purple files at first?
2. How many files were in the box in the end?

	Blue	Grey	Purple	White	Total
Before	5 u	2 u	3 u + 15	0	205
Change 1	No change	No change	- 15		- 15
After 1	5 u	2 u	3 u		190
Change 2	No change	No change	No change	+ 4 u
After 2	5 u	2 u	3 u	4 u

(a)
Total number of files at first
= 5 u + 2 u + 3 u + 15
= 10 u + 15

10 u + 15 = 205
10 u = 205 - 15
10 u = 190

1 u = 190 ÷ 10 = 19

Number of blue files at first
= 5 u
= 5 x 19
= 95

Number of grey files at first
= 2 u
= 2 x 19
= 38

Number of purple files at first
= 3 u + 15
= 3 x 19 + 15
= 72 

At first
Blue files : Grey files : Purple files
95 : 38 : 72

(b)
Total number of files in the box in the end
= 5 u + 2 u + 3 u + 4 u
= 14 u
= 266

Answer(s): (a) 95 : 38 : 72; (b) 266