A shopkeeper divides an ice-cream brick into two halves, then cuts one of the…
2024
A shopkeeper divides an ice-cream brick into two halves, then cuts one of the halves into several smaller portions of equal size. Each of the smaller portions weighs 12 grams. The shopkeeper now has a total of 5 portions. How heavy was the original brick?
- A.
100 grams
- B.
96 grams
- C.
98 grams
- D.
95 grams
Show answer & explanation
Correct answer: B
Concept: when an object is split into two equal halves, and one half is further cut into several identical smaller portions, the total weight of that half equals the count of small portions multiplied by each portion's weight (cutting only redistributes mass, it never changes it). Doubling that half's weight then recovers the weight of the whole original object, since both halves are equal.
The 5 total portions consist of the one untouched half plus the pieces cut from the other half.
So the cut half was divided into 5 minus 1, i.e. 4, equal-sized smaller portions.
Each small portion weighs 12 grams, so the cut half weighs 4 times 12 = 48 grams.
Since the brick was divided into two equal halves, the untouched half also weighs 48 grams.
Total weight of the original brick = 48 + 48 = 96 grams.
Cross-check: 4 small portions of 12 grams (48 grams) plus the 1 untouched half (48 grams) gives 5 portions in total, consistent with both the stated portion count and the equal-halves constraint.