A man sells different brands of an item. 1/9 of the items he has in his shop are from Brand A, 5/8 o

Let the total number of items be T. Brand A takes 1/9 of T, so the remainder left is 1 − 1/9 = 8/9 of T.

Brand B is 5/8 of that remainder: 5/8 × 8/9 T = 5/9 T. Brand C is what is left of the remainder: 8/9 T − 5/9 T = 3/9 T = 1/3 T.

We are told Brand C items are 81, so 1/3 × T = 81, which gives T = 81 × 3 = 243 items in all. Then Brand B = 5/9 × 243 = 5 × 27 = 135 items. (Quick check: Brand A = 1/9 × 243 = 27, and 27 + 135 + 81 = 243. ✓)

The question asks how many MORE Brand B items there are than Brand C: 135 − 81 = 54. So the shop has 54 more Brand B items than Brand C. Watch the wording here — 243 is the total, and 135 is just the Brand B count, so neither of those answers the question asked.