There were 200 yellow, brown and green files in a box. 10 green files were removed from the box and the ratio of the number of yellow files to the number of brown files to the number of green files became 3 : 2 : 5. Then some pink files were added and the ratio of the number of green files to the number of pink files was 5 : 2.

1. What was the ratio of the number of yellow files to the number of brown files to the number of green files at first?
2. How many files were in the box in the end?

	Yellow	Brown	Green	Pink	Total
Before	3 u	2 u	5 u + 10	0	200
Change 1	No change	No change	- 10		- 10
After 1	3 u	2 u	5 u		190
Change 2	No change	No change	No change	+ 2 u
After 2	3 u	2 u	5 u	2 u

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

10 u + 10 = 200
10 u = 200 - 10
10 u = 190

1 u = 190 ÷ 10 = 19

Number of yellow files at first
= 3 u
= 3 x 19
= 57

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

Number of green files at first
= 5 u + 10
= 5 x 19 + 10
= 105 

At first
Yellow files : Brown files : Green files
57 : 38 : 105

(b)
Total number of files in the box in the end
= 3 u + 2 u + 5 u + 2 u
= 12 u
= 228

Answer(s): (a) 57 : 38 : 105; (b) 228