Solve this multiple-choice question and choose the correct option.

Concept & Cost Price Calculation: Cost price (CP) can be calculated if we have the selling price (SP) and the profit relationship. SP = CP + Profit Step-by-Step Solution: 1. Analyze the Question: We need to find the numerical value of the Cost Price (CP). 2. Evaluate Statement I: "The profit earned on the article is one-third of the cost price." This means Profit = (1/3) × CP. This gives a ratio but no absolute value. Not sufficient alone. 3. Evaluate Statement II: "The article is sold for ₹ 400." This gives SP = ₹ 400. No information about profit or CP. Not sufficient alone. 4. Evaluate Both Statements Together: From I: Profit = (1/3) CP From II: SP = 400 We know SP = CP + Profit 400 = CP + (1/3) CP 400 = (4/3) CP CP = (400 × 3/4) = 300 We can calculate the exact CP. Therefore, both statements together are necessary. Exam Strategy & Shortcut: Statement I gives a relative value (ratio), Statement II gives an absolute value. Combining them allows solving for the unknown. Common Pitfall: Assuming a fractional profit gives the absolute value without a base selling price or cost price. Final Answer: Therefore, the correct answer is if the data in both Statements I and II together are necessary to answer the question.

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 is the cost price of the article? I. The profit earned on the article is one-third of the cost price. II. The article is sold for ₹ 400.

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

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

if the data either in Statement I or in Statement II alone are sufficient to answer the question

if the data even in both Statements I and II together are not sufficient to answer the question

[Solved] Directions: Each of the questions given below

Answer

Correct Answer: if the data in both Statements I and II together are necessary to answer the question

Explanation

### Concept & Cost Price Calculation Cost price (CP) can be calculated if we have the selling price (SP) and the profit relationship. $$SP = CP + Profit$$ ### Step-by-Step Solution 1. **Analyze the Question:** We need to find the numerical value of the Cost Price (CP). 2. **Evaluate Statement I:** "The profit earned on the article is one-third of the cost price." This means $Profit = \frac{1}{3} \times CP$. This gives a ratio but no absolute value. Not sufficient alone. 3. **Evaluate Statement II:** "The article is sold for $₹ 400$." This gives $SP = ₹ 400$. No information about profit or CP. Not sufficient alone. 4. **Evaluate Both Statements Together:** From I: $Profit = \frac{1}{3} CP$ From II: $SP = 400$ We know $SP = CP + Profit$ $$400 = CP + \frac{1}{3} CP$$ $$400 = \frac{4}{3} CP$$ $$CP = \frac{400 \times 3}{4} = 300$$ We can calculate the exact CP. Therefore, both statements together are necessary. ### Exam Strategy & Shortcut Statement I gives a relative value (ratio), Statement II gives an absolute value. Combining them allows solving for the unknown. ### Common Pitfall Assuming a fractional profit gives the absolute value without a base selling price or cost price. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question**.