Difficulty: Easy
Correct Answer: 10%
Explanation:
Introduction / Context:
This is a direct ratio based profit question. Instead of giving the actual cost and selling prices, the question provides their ratio. From this, you must determine the profit percentage. Such ratio forms are common in aptitude tests because they simplify arithmetic while still checking your understanding of how profit percent is defined.
Given Data / Assumptions:
Concept / Approach:
If CP : SP = 10 : 11, we can assume CP = 10 units and SP = 11 units. Profit is SP - CP in the same units. Profit percent is then (Profit / CP) * 100. This approach of working with proportional units instead of actual rupees is a standard shortcut in ratio problems.
Step-by-Step Solution:
Given CP : SP = 10 : 11.Assume CP = 10 units and SP = 11 units.Profit = SP - CP = 11 - 10 = 1 unit.Profit percentage = (Profit / CP) * 100.Profit percentage = (1 / 10) * 100 = 10%.Therefore the profit made is 10%.
Verification / Alternative check:
Take a concrete example: let CP be Rs 100. From the ratio 10 : 11, SP must be Rs 110. Profit is Rs 10 on a cost of Rs 100, so percentage profit = 10 / 100 * 100 = 10%. This matches our earlier unit based calculation and confirms the result.
Why Other Options Are Wrong:
1% profit would arise if SP were 10.1 for CP 10, 5% if SP were 10.5, and 8% if SP were 10.8 given CP of 10. None of these matches the ratio 10 : 11. Only 10% profit matches the CU ratio of 10 : 11 for cost and selling prices.
Common Pitfalls:
Students sometimes invert the ratio and treat it as SP : CP instead of CP : SP, which would lead to a completely different answer. Carefully reading the statement and assigning the ratio correctly is very important. Another mistake is to confuse profit percentage with the ratio of SP to CP directly without subtracting CP from SP first.
Final Answer:
The profit percentage on the article is 10%.
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