A man sells different brands of an items 1 9 of... - JAMB Mathematics 2023 Question
A man sells different brands of an items. \(^1/_9\) of the items he has in his shop are from Brand A, \(^5/_8\) of the remainder are from Brand B and the rest are from Brand C. If the total number of Brand C items in the man\'s shop is 81, how many more Brand B items than Brand C does the shop has?
243
108
54
135
1. Let \(y\) be the total number of items in the man's shop.
2. \(^1/_9\) of the items are from Brand A: \(\frac{1}{9}y\).
3. The remainder is \(\frac{8}{9}y\).
4. \(^5/_8\) of the remainder are from Brand B: \(\frac{5}{8} \times \frac{8}{9}y = \frac{5}{9}y\).
5. Total items from Brand A and Brand B: \(\frac{1}{9}y + \frac{5}{9}y = \frac{2}{3}y\).
6. Remaining items (Brand C): \(1 - \frac{2}{3}y = \frac{1}{3}y\).
7. Given that the number of Brand C items is 81: \(\frac{1}{3}y = 81\).
8. Solve for \(y\): \(y = 81 \times 3 = 243\).
9. Number of Brand B items: \(\frac{5}{9} \times 243 = 135\).
10. The number of more Brand B items than Brand C: \(135 - 81 = 54\).
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