A lady wants to buy the following items in the given price range- 1. Tomato between Rs. 40 and Rs. 45 per kg. 2. Grapes in the price range of Rs. 80 and Rs. 90 per kg. 3. Milk packets at Rs. 23 per liter. In which shop from the following will she definitely get all her items/ A. Shop S sells tomato at Rs. 22.5 per half kg, Grapes at Rs. 82 per kg and milk at Rs. 24 per liter. B. Shop H sells grapes at Rs. 21 per quarter kg, milk at 12.5 per half litre and tomato at Rs. 22 per half kg. C. Shop O sells milk at Rs. 11.5 per half litre, tomato at 21 per half kg and grapes at Rs. 43 per half kg.
C
Finding the Right Shop: Price Range Analysis
This question asks us to identify which shop among the given options sells all the required items within a lady's specific price range or at a precise price.
The lady wants to buy the following items with these price constraints:
- Tomato: Between Rs. 40 and Rs. 45 per kg (inclusive).
- Grapes: Between Rs. 80 and Rs. 90 per kg (inclusive).
- Milk packets: Exactly Rs. 23 per liter.
We need to evaluate each shop option by converting their listed prices to the standard units (per kg for tomato and grapes, per liter for milk) and check if they fall within the desired range or meet the exact price requirement.
Analyzing Shop A Prices
- Tomato: Rs. 22.5 per half kg.
Price per kg = $\text{Rs. } 22.5 \times 2 = \text{Rs. } 45$ per kg.
Is Rs. 45 between Rs. 40 and Rs. 45? Yes, it is within the range.
- Grapes: Rs. 82 per kg.
Is Rs. 82 between Rs. 80 and Rs. 90? Yes, it is within the range.
- Milk: Rs. 24 per liter.
Is Rs. 24 exactly Rs. 23? No.
Shop A does not sell milk at the required price. So, Shop A is not the correct answer.
Analyzing Shop H Prices
- Grapes: Rs. 21 per quarter kg (0.25 kg).
Price per kg = $\text{Rs. } 21 \times 4 = \text{Rs. } 84$ per kg.
Is Rs. 84 between Rs. 80 and Rs. 90? Yes, it is within the range.
- Milk: Rs. 12.5 per half litre (0.5 litre).
Price per liter = $\text{Rs. } 12.5 \times 2 = \text{Rs. } 25$ per liter.
Is Rs. 25 exactly Rs. 23? No.
- Tomato: Rs. 22 per half kg.
Price per kg = $\text{Rs. } 22 \times 2 = \text{Rs. } 44$ per kg.
Is Rs. 44 between Rs. 40 and Rs. 45? Yes, it is within the range.
Shop H does not sell milk at the required price. So, Shop H is not the correct answer.
Analyzing Shop O Prices
- Milk: Rs. 11.5 per half litre.
Price per liter = $\text{Rs. } 11.5 \times 2 = \text{Rs. } 23$ per liter.
Is Rs. 23 exactly Rs. 23? Yes.
- Tomato: Rs. 21 per half kg.
Price per kg = $\text{Rs. } 21 \times 2 = \text{Rs. } 42$ per kg.
Is Rs. 42 between Rs. 40 and Rs. 45? Yes, it is within the range.
- Grapes: Rs. 43 per half kg.
Price per kg = $\text{Rs. } 43 \times 2 = \text{Rs. } 86$ per kg.
Is Rs. 86 between Rs. 80 and Rs. 90? Yes, it is within the range.
Shop O sells all items (Tomato, Grapes, and Milk) within the lady's desired price range or at the exact required price. So, Shop O is a potential answer.
Analyzing Shop P Prices
- Tomato: Rs. 23.5 per half kg.
Price per kg = $\text{Rs. } 23.5 \times 2 = \text{Rs. } 47$ per kg.
Is Rs. 47 between Rs. 40 and Rs. 45? No, it is outside the range.
- Grapes: Rs. 85 per kg.
Is Rs. 85 between Rs. 80 and Rs. 90? Yes, it is within the range.
- Milk: Rs. 23 per litre.
Is Rs. 23 exactly Rs. 23? Yes.
Shop P does not sell tomato within the required price range. So, Shop P is not the correct answer.
Summary of Shop Prices vs. Required Prices
| Item | Required Price | Shop A Price (per kg/liter) | Shop H Price (per kg/liter) | Shop O Price (per kg/liter) | Shop P Price (per kg/liter) |
|---|---|---|---|---|---|
| Tomato | Rs. 40 - 45/kg | Rs. 45/kg (OK) | Rs. 44/kg (OK) | Rs. 42/kg (OK) | Rs. 47/kg (Not OK) |
| Grapes | Rs. 80 - 90/kg | Rs. 82/kg (OK) | Rs. 84/kg (OK) | Rs. 86/kg (OK) | Rs. 85/kg (OK) |
| Milk | Rs. 23/liter | Rs. 24/liter (Not OK) | Rs. 25/liter (Not OK) | Rs. 23/liter (OK) | Rs. 23/liter (OK) |
Based on the analysis, only Shop O meets the price requirements for all three items.
Conclusion on Finding the Right Shop
By carefully examining the prices offered at each shop and comparing them against the lady's desired price ranges and exact price for milk, we found that only Shop O sells Tomato between Rs. 40 and Rs. 45 per kg, Grapes between Rs. 80 and Rs. 90 per kg, and Milk at exactly Rs. 23 per liter. Therefore, the lady will definitely get all her items from Shop O.
Revision Table: Shop Price Analysis Summary
| Shop | Tomato (Rs. 40-45/kg) | Grapes (Rs. 80-90/kg) | Milk (Rs. 23/liter) | Can get all items? |
|---|---|---|---|---|
| A | Rs. 45 (OK) | Rs. 82 (OK) | Rs. 24 (Not OK) | No |
| H | Rs. 44 (OK) | Rs. 84 (OK) | Rs. 25 (Not OK) | No |
| O | Rs. 42 (OK) | Rs. 86 (OK) | Rs. 23 (OK) | Yes |
| P | Rs. 47 (Not OK) | Rs. 85 (OK) | Rs. 23 (OK) | No |
This table clearly shows that only Shop O satisfies all three price conditions simultaneously.
Additional Information on Price Range Problems
Problems involving price ranges require careful conversion of given prices to a common unit (like per kg or per liter) before comparison. It's important to understand what "between X and Y" means. If inclusive, it includes X and Y; if exclusive, it does not. In this question, the wording implies inclusivity for the ranges.
- Always convert units to match the requirement (e.g., half kg price to kg price).
- Pay attention to whether a price needs to be exactly a certain value or within a range.
- Check each condition for every option thoroughly.
- Only an option satisfying ALL conditions is the correct answer.
These types of questions test your ability to perform simple unit conversions and evaluate multiple conditions simultaneously based on given constraints.
Important Questions from Data Sufficiency
Which of the following statement is correct?
I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.
II. The value of
\(\left(k^2+ \frac{1}{k^2} \right) \left(k- \frac{1}{k} \right) \left(k^4+ \frac{1}{k^4} \right) \) \(\left(k+ \frac{1}{k} \right)\left(k^4- \frac{1}{k^4} \right)\) is \(k^{16}- \frac{1}{k^{16}}\).
Given below is a question followed by two statements I and II. Read both statements carefully to decide which one of them is sufficient to answer the question.
Six people - A, B, C, D, E and F are sitting in a straight line facing north. Who sits to the immediate left of D?
(I) A sits second from one of the extreme ends of the line. Only two people sit between A and B. E sits to the immediate right of C.
(II) C sits third from the left end of the line. Only one person sits between C and F. E sits third to the right of F.
Please read the below equation and select an appropriate option from the following.
x + y = 10 ; y = x - 2
Quantity A is x.
Quantity B is y.
You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
When is Yuvi's wedding anniversary?
Statements:
1: On the 7 th day of a month.
2. The month has 29 days only in a leap year.
One question and three statements are numbered (I), (II) and (III). You have to decide whether the facts given in the statements are sufficient to answer the question given below.
Question: What is the length of the rectangle?
Statement:
I. The perimeter of the rectangle is 80 meters.
II. The sum of the adjacent sides is 40 meters.
III. The width of the rectangle is 10 meters.
Choose the correct option.
A. Only I is sufficient.
B. Only I and II are sufficient.
C. III and one from I or II are sufficient.
D. II and one from I or III are sufficient.
