A small shop owner keeps inventory satisfying the following criteria – 1. Shampoo sachets that are priced between Rs.4 and Rs.10 per sachet. 2. Chocolates in the price range of Re.1 and Rs.60 per piece. 3. Dry fruits priced more than Rs.125 per 100 grams. 4. Milk packets in the price range of Rs.21 and Rs.29 per litre. Which list among the following will definitely NOT be found in his shop?
Shop Inventory Price Criteria
A shop owner has specific price ranges for the inventory items. We need to determine which option violates these rules. The criteria are:
- Shampoo sachets: Price between Rs. 4 and Rs. 10 (inclusive).
LaTeX: $Rs. 4 \le price \le Rs. 10$ - Chocolates: Price between Re. 1 and Rs. 60 (inclusive).
LaTeX: $Rs. 1 \le price \le Rs. 60$ - Dry fruits: Priced more than Rs. 125 per 100 grams.
LaTeX: $price \text{ per } 100 \text{g} > Rs. 125$ - Milk packets: Price between Rs. 21 and Rs. 29 (inclusive).
LaTeX: $Rs. 21 \le price \le Rs. 29$
Evaluating Product Lists Against Criteria
Let's check each option against the defined inventory rules:
Option 1 Verification
This list includes:
- Shampoo A at Rs. 4 (within Rs. 4-10 range).
- Chocolate B at Rs. 1.5 (within Rs. 1-60 range).
- Dry fruit C at Rs. 250 per 125 grams. The price per 100 grams is calculated as:
LaTeX: $\left( \frac{Rs. 250}{125 \text{g}} \right) \times 100 \text{g} = Rs. 200 \text{ per } 100 \text{g}$. This is greater than Rs. 125.
All items in Option 1 meet the shop's criteria.
Option 2 Verification
This list includes:
- Shampoo P at Rs. 5 (within Rs. 4-10 range).
- Milk packet Q at Rs. 23 (within Rs. 21-29 range).
- Dry fruit R at Rs. 150 per 100 grams. This is greater than Rs. 125.
All items in Option 2 meet the shop's criteria.
Option 3 Verification
This list includes:
- Shampoo X at Rs. 5 (within Rs. 4-10 range).
- Chocolate Y at Rs. 1 (within Rs. 1-60 range).
- Dry fruit Z at Rs. 100 per 100 grams. The price per 100 grams is Rs. 100. This is NOT more than Rs. 125.
The dry fruit in Option 3 does NOT meet the shop's criteria.
Option 4 Verification
This list includes:
- Shampoo L at Rs. 4 (within Rs. 4-10 range).
- Milk packet M at Rs. 24.5 (within Rs. 21-29 range).
- Chocolate N at Rs. 35 (within Rs. 1-60 range).
- Dry fruit O at Rs. 350 per 200 grams. The price per 100 grams is calculated as:
LaTeX: $\left( \frac{Rs. 350}{200 \text{g}} \right) \times 100 \text{g} = Rs. 175 \text{ per } 100 \text{g}$. This is greater than Rs. 125.
All items in Option 4 meet the shop's criteria.
Conclusion on Inventory Exclusion
The question asks which list will definitely NOT be found. Option 3 fails because the dry fruit Z is priced at Rs. 100 per 100 grams, which does not meet the criterion of being more than Rs. 125 per 100 grams.
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