A packet contained brown, yellow and blue files. ³₅ of the files were brown and ⁴₉ of the remainder were yellow files.The rest were blue files.

1. Find the ratio of the number of blue files to the number of brown files.
2. There were 190 fewer yellow files than brown files. How many files were there in the packet?

Brown files	Yellow files	Blue files
3x9	2x9
	4x2	5x2
27 u	8 u	10 u

(a)
Fraction of brown files = ³₅
Fraction of files that are not brown = 1 - ³₅ = ²₅

Remaining fraction of yellow files = ⁴₉
Remaining fraction of blue files = 1 - ⁴₉ = ⁵₉

The total number of yellow files and blue files is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 2 and 9 = 18

Blue files : Brown files
10 : 27

(b)
Difference in the number of brown files and yellow files
= 27 u - 8 u
= 19 u

19 u = 190
1 u = 190 ÷ 19 = 10

Total number of files
= 27 u + 8 u + 10 u
= 45 u
= 45 x 10
= 450

Answer(s): (a) 10 : 27; (b) 450