There were 73 white, purple and black files in a box. 7 black files were removed from the box and the ratio of the number of white files to the number of purple files to the number of black files became 4 : 2 : 5. Then some brown files were added and the ratio of the number of black files to the number of brown files was 5 : 3.

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

	White	Purple	Black	Brown	Total
Before	4 u	2 u	5 u + 7	0	73
Change 1	No change	No change	- 7		- 7
After 1	4 u	2 u	5 u		66
Change 2	No change	No change	No change	+ 3 u
After 2	4 u	2 u	5 u	3 u

(a)
Total number of files at first
= 4 u + 2 u + 5 u + 7
= 11 u + 7

11 u + 7 = 73
11 u = 73 - 7
11 u = 66

1 u = 66 ÷ 11 = 6

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

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

Number of black files at first
= 5 u + 7
= 5 x 6 + 7
= 37 

At first
White files : Purple files : Black files
24 : 12 : 37

(b)
Total number of files in the box in the end
= 4 u + 2 u + 5 u + 3 u
= 14 u
= 84

Answer(s): (a) 24 : 12 : 37; (b) 84