Brain Teasers
Romankachi Stationery!
Fun: (2.16)
Difficulty: (2.2)
Puzzle ID: #18961
Submitted By: lesternoronha1 Corrected By: MarcM1098
Submitted By: lesternoronha1 Corrected By: MarcM1098
One of my very close friends, Raimo the shrewd has opened a new stationery store called "The Romankachi Bookstore" in honor of my grandfather Rudolf the world-famous Romankachi who had helped him a lot financially in recent times. Among other stationery items, pencils, erasers and sharpeners were available at this shop.
Raimo told me that he could make profits in pencils, erasers and sharpeners only by adhering to the following:
1) A pencil, an eraser and a sharpener together to cost 7k (k being Kachin, the local Romankachi currency).
2) The cost of a sharpener would be more than that of 3 erasers.
3) No two items among pencils, erasers and sharpeners would be sold at the same cost.
If all the costs are integers, can you look through Raimo's shrewdness and find out the cost of each of the stationery items mentioned above?
Raimo told me that he could make profits in pencils, erasers and sharpeners only by adhering to the following:
1) A pencil, an eraser and a sharpener together to cost 7k (k being Kachin, the local Romankachi currency).
2) The cost of a sharpener would be more than that of 3 erasers.
3) No two items among pencils, erasers and sharpeners would be sold at the same cost.
If all the costs are integers, can you look through Raimo's shrewdness and find out the cost of each of the stationery items mentioned above?
Answer
It has been mentioned that all the costs are integers and no two items cost the same.Also
1) A pencil, an eraser and a sharpener together to cost 7k.
2) The cost of a sharpener would be more than that of 3 erasers.
Now, let the cost of a pencil, an eraser and a sharpener be X, Y and Z respectively.
Then X+Y+Z = 7 from condition 1 above.
Also Z > 3Y from condition 2 above.
Let the cost of each eraser Y=1, the smallest possible integer.
Then Z > 3 (from condition 2).
Let us consider the different values that Z can take:
Let Z=4.
Then X = 7-Y-Z (from equation X+Y+Z = 7).
Then X = 7-1-4 = 2
Hence X = 2, Y = 1 and Z = 4.
Let Z=5.
Then X+Y = 2 (from equation X+Y+Z = 7).
Hence X = Y = 1.
This cannot be possible since it has been mentioned that no two items cost the same.
For any higher values of Z, we do not get integer values for X and Y.
Hence each pencil, eraser and sharpener must cost 2k, 1k and 4k respectively.
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