Directions: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What would have been the selling price per kg of rice? I. 50 kg of rice was purchased for ₹ 3350 and ₹ 150 were spent on transport. II. Profit earned was 5%.
Verbal Reasoning
Data Sufficiency
Difficulty: Easy
Choose an option
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Aif the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question;
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Bif the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question;
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Cif the data either in Statement I or in Statement II alone are sufficient to answer the question;
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Dif the data even in both Statements I and II together are not sufficient to answer the question;
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Eif the data in both Statements I and II together are necessary to answer the question.
Answer
Correct Answer: if the data in both Statements I and II together are necessary to answer the question.
Explanation
### Concept & Logic
To find the Selling Price (SP) per unit, you need the Total Cost Price (including overheads) per unit and the Profit Percentage (or absolute profit per unit).
$$ \text{Total Cost Price} = \text{Purchase Price} + \text{Overheads (Transport)} $$
$$ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit \%}}{100}\right) $$
### Step-by-Step Solution
We need the SP per kg.
- Evaluating Statement I: Total Cost = $3350 + 150 = 3500$ for 50 kg. Therefore, CP per kg = $\frac{3500}{50} = \text{₹ } 70$. However, without knowing the profit or loss margin, we cannot determine the Selling Price. Insufficient.
- Evaluating Statement II: It states the profit earned was $5\%$. Without knowing the Cost Price, this percentage cannot be applied to find an absolute Selling Price. Insufficient.
- Combining I and II: We have CP per kg (₹ 70) and Profit Percentage ($5\%$). We can calculate the SP per kg as $70 \times 1.05 = \text{₹ } 73.5$.
- Both statements together are required to find the exact selling price per kg.
### Exam Strategy & Shortcut
Identify the missing variables. The question asks for SP. Statement I gives total CP. Statement II gives Profit %. Both pieces (CP and Profit margin) are strictly necessary to calculate SP.
### Common Pitfall
Forgetting to include the transport cost (overheads) into the total Cost Price. Overheads are always added to the initial purchase price before calculating profit.
### Final Answer
Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question.**