Difficulty: Easy
Correct Answer: 5 : 6
Explanation:
Introduction / Context:
This is a basic profit and loss question that checks whether you can convert a given profit percentage into a simple ratio between cost price and selling price. Understanding this relationship is useful because many competitive exam questions are framed in terms of ratios instead of explicit prices.
Given Data / Assumptions:
Concept / Approach:
By definition, profit percentage = (Profit / CP) * 100. If profit is 20%, then SP = CP + 20% of CP. That is SP = CP * (1 + 20/100) = CP * 1.2. By choosing a convenient CP value, we can represent both CP and SP as whole numbers and obtain the CP : SP ratio. Since percentage is relative, the choice of CP does not affect the final ratio.
Step-by-Step Solution:
Assume CP = 100 units (for convenience).
Profit at 20% = 20% of 100 = 20 units.
Selling price SP = CP + profit = 100 + 20 = 120 units.
Thus, CP : SP = 100 : 120.
Divide both terms by 20 to simplify the ratio: (100 / 20) : (120 / 20) = 5 : 6.
Verification / Alternative check:
We can also use direct multiplication: SP = 1.2 * CP. Treat CP = 5, then SP = 1.2 * 5 = 6. Hence CP : SP = 5 : 6, which confirms the same ratio. Any other assumed cost price will yield an equivalent ratio that simplifies to 5 : 6.
Why Other Options Are Wrong:
The ratio 4 : 5 corresponds to a 25% profit, not 20%. The ratio 2 : 5 implies an extreme profit that is not consistent with 20%. The ratio 3 : 4 corresponds to a profit of 33.33%, which is also incorrect for 20% profit. Therefore, only 5 : 6 correctly represents a 20% profit.
Common Pitfalls:
Learners sometimes reverse the ratio and write SP : CP instead of CP : SP. Others may incorrectly add 20 to both numbers instead of working with percentages. Always remember that profit percentage relates to cost price, and the ratio must be simplified after calculating SP from CP.
Final Answer:
The required ratio of cost price to selling price at 20% profit is 5 : 6.
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