A total of 20 white files and blue files are in a container. The ratio of white files to blue files was 1 : 9. Some pink files and black files were put into the container. For every 3 blue files that were already in the container, 13 black ones were added. Then, the final number of white files and pink files was ¹₄ the final number of blue files and black files. Find the total number of pink and black files.

Pink files	White files	Blue files	Black files
	1x1	9x1
		3x3	13x3
1x12		4x12
11 u	1 u	9 u	39 u

The number of blue files is repeated.  Make the number of blue files the same.  LCM of 9 and 3 is 9.

The total number of blue files and black files is repeated.  Make the total number of blue and black files the same.  LCM of 48 and 4 is 48.

Total number of white files and blue files
= 1 u + 9 u
= 10 u

10 u = 20

1 u = 20 ÷ 10 = 2

Total number of pink and black files
= 11 u + 39 u
= 50 u
= 50 x 2
= 100

Answer(s): 100