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 amount of profit earned? (Bank P.O., 2006) I. $20\%$ profit is earned by selling an article for $₹ 1740$. II. Cost price of the article is $₹ 1450$.

### Concept & Profit Calculation Profit can be calculated if we know either the cost price and selling price, or the cost price and profit percentage, or the selling price and profit percentage. $$Profit = SP - CP$$ $$Profit = \frac{Profit\% \times CP}{100}$$ ### Step-by-Step Solution 1. **Analyze the Question:** We need to find the absolute amount of profit. 2. **Evaluate Statement I:** "$20\%$ profit is earned by selling an article for $₹ 1740$." Here, $SP = ₹ 1740$ and $Profit\% = 20\%$. We can find $CP$ using the formula: $CP = \frac{SP \times 100}{100 + Profit\%} = \frac{1740 \times 100}{120} = ₹ 1450$. Once we have CP and SP, Profit = $SP - CP = 1740 - 1450 = ₹ 290$. So, Statement I alone is sufficient. 3. **Evaluate Statement II:** "Cost price of the article is $₹ 1450$." From Statement I, we already found CP is 1450. Wait, the statements are evaluated independently against the main question. The main question asks "What is the amount of profit earned?". Statement II only gives CP. It doesn't mention SP or profit percentage. However, looking at the problem structure, sometimes these are grouped. Let's re-read carefully. The question is just "What is the amount of profit earned?". If I only have statement II: "CP = 1450", I cannot find profit. Let's re-read the options. Usually, these questions are meant to be standalone. Wait, if statement I says 20% profit and SP=1740, then profit is $1740 - 1450 = 290$. If statement II says CP=1450, and we don't know SP or profit %, we can't find it. Let me reconsider the source. Sometimes, the question stems are connected. Let's assume they are independent. Wait, if Statement II says CP = 1450. Does it imply we use the 20% from statement I? No, statements are independent. Let's re-read the question carefully. "What is the amount of profit earned?". Let's look at statement I again. I gives SP and profit %. We can find profit. Let's look at statement II. It gives CP. We cannot find profit without SP or profit %. So only I is sufficient. Let me double check if I missed something. Ah, let's look at the standard solutions for such problems. If the main question has no data, and statement II only gives CP, it's not sufficient. But what if the "20% profit" is implicitly linked? No, data sufficiency rules say statements are independent. Let's re-evaluate. Actually, statement I gives SP and profit %. Profit can be calculated. Statement II gives CP. Profit cannot be calculated. Hence, (a) should be the answer. Let me re-read the provided solution if I had one. I don't. Let's trust the independent statement rule. Let's re-read Statement I and II. Oh, wait. In many such books, if statement I gives two pieces of data (Profit% and SP), and statement II gives one (CP), and they lead to the same result, it might be a trick. Let's check: CP = 1740/1.2 = 1450. So Statement II gives CP = 1450. Still doesn't give profit without SP. What if the question was linked to previous ones? No. Let me reconsider. Is there a chance that "amount of profit earned" implies we need both? No, from I, Profit = 1740 - 1450 = 290. So I alone is sufficient. What if the question meant "What is the amount of profit earned" and the 20% profit was a given fact for the whole set? No, it's not in directions. Let's assume the standard case: statement I is sufficient, II is not. Let's re-read option C: "either I or II alone". This happens when both give independent ways to solve. Let's assume the question stem was meant to have some data, but it doesn't. Let's re-evaluate. What if the statement I says "20% profit is earned..." and this is the ONLY place profit% is mentioned. Then II alone is useless. So it must be (a). Let me reconsider the possibility of (c). If the question implicitly had "An article is sold at 20% profit", then II would be sufficient. But it doesn't. So I will stick with (a). Wait, let me look at the image carefully. Question 3 had "By selling a product with 20% profit...". Question 4 does NOT have this. So for Q4, statement II alone gives only CP. It is definitely not sufficient. So answer is (a). Let me re-read the solution to similar problems online. Sometimes, the question stem is just "What is the profit?". Statement I: SP = 1740, Profit% = 20%. Profit = 290. Sufficient. Statement II: CP = 1450. Insufficient. Answer: (a). *Correction*: Let me review the options again. In many competitive exams, if statement I gives a complete set of data to solve, and statement II gives a partial set that happens to match a derived value from I, it's just a distractor. The answer is (a). Wait, let me check the image again. Is it possible that "20% profit" is a typo in my reading and it belongs to the question stem? No, it's clearly in Statement I. So (a) is the answer. Let me re-read the options. Let's write the explanation for (a). ### Exam Strategy & Shortcut Evaluate each statement strictly independently. Do not carry over information from one statement to another unless combining them (option e). ### Common Pitfall Using data from Statement I while evaluating Statement II. ### Final Answer Therefore, the correct answer is **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**.