There were 103 purple, black and blue files in a box. 13 blue files were removed from the box and the ratio of the number of purple files to the number of black files to the number of blue files became 4 : 2 : 9. Then some white files were added and the ratio of the number of blue files to the number of white files was 9 : 5.

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

	Purple	Black	Blue	White	Total
Before	4 u	2 u	9 u + 13	0	103
Change 1	No change	No change	- 13		- 13
After 1	4 u	2 u	9 u		90
Change 2	No change	No change	No change	+ 5 u
After 2	4 u	2 u	9 u	5 u

(a)
Total number of files at first
= 4 u + 2 u + 9 u + 13
= 15 u + 13

15 u + 13 = 103
15 u = 103 - 13
15 u = 90

1 u = 90 ÷ 15 = 6

Number of purple files at first
= 4 u
= 4 x 6
= 24

Number of black files at first
= 2 u
= 2 x 6
= 12

Number of blue files at first
= 9 u + 13
= 9 x 6 + 13
= 67 

At first
Purple files : Black files : Blue files
24 : 12 : 67

(b)
Total number of files in the box in the end
= 4 u + 2 u + 9 u + 5 u
= 20 u
= 120

Answer(s): (a) 24 : 12 : 67; (b) 120