John bought a TV from an online sale for 15,000 INR.
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John bought a TV from an online sale for 15,000 INR. He then sold the TV to his friend Jamie. Which of the following statements is/are sufficient to determine if John made a profit on the sale?
- Statement I: Jamie sold the TV to his friend Jake for 20,000 INR.
- Statement II: Jamie was given a discount of 20% on the marked price.
- Statement III: John pasted a price tag (marked price) of 25,000 INR on the TV.
Show answer & explanation
To determine if John made a profit, we need to find the price at which John sold the TV to Jamie. Statement III provides the marked price, and Statement II provides the discount percentage applied to that marked price, allowing us to calculate the actual selling price.
Step-by-step Derivation:
Step 1: Identify the cost price (CP) for John. CP = 15,000 INR.
Step 2: Analyze Statement I: Jamie sold the TV to Jake for 20,000 INR. This is the transaction between Jamie and Jake, which does not provide information about the transaction between John and Jamie. Thus, Statement I is irrelevant.
Step 3: Analyze Statement II: Jamie received a 20% discount on the marked price. This tells us the selling price (SP) = Marked Price * (1 - 0.20). However, the marked price is unknown.
Step 4: Analyze Statement III: John set the marked price at 25,000 INR. This provides the missing value for Statement II.
Step 5: Combine Statement II and III: SP = 25,000 * (1 - 0.20) = 25,000 * 0.80 = 20,000 INR.
Step 6: Compare SP to CP: Since SP (20,000 INR) > CP (15,000 INR), John made a profit of 5,000 INR.
Step 7: Conclusion: Statements II and III together are sufficient to determine the profit.