Out of the 6B-Pencils sold by stores B and C, 40% and 20% respectively are…

Concept: When a total is divided between two categories in the ratio a : b, one part fixes the other — the second quantity equals the first multiplied by b/a. A percentage return acts only on the category it is stated for, so the net quantity sold equals every item recorded as sold minus the stated percentage of that one category alone.

Application

1. Store B sells 480 HB-pencils with HB : 6B = 6 : 5, so its 6B-pencils = 480 × 5/6 = 400.

2. Store C sells 400 HB-pencils with HB : 6B = 4 : 1, so its 6B-pencils = 400 × 1/4 = 100.

3. Pencils recorded as sold before any return = (480 + 400) for B and (400 + 100) for C = 880 + 500 = 1380.

4. Defective 6B-pencils returned to B = 40% of 400 = 160; returned to C = 20% of 100 = 20; together 160 + 20 = 180.

5. Pencils actually sold = 1380 − 180 = 1200.

Cross-check: Netting each store on its own gives 880 − 160 = 720 for B and 500 − 20 = 480 for C, and 720 + 480 = 1200 — the same total reached above. The HB-pencils, 480 + 400 = 880, carry no returns at all, so only the 6B column is reduced; a common slip is to apply the 40% and 20% to a store’s whole sale instead of to its 6B-pencils alone.