Profit and Loss — The selling price of 20 articles equals the cost price of 22 articles. Determine the gain percentage.

Difficulty: Easy

Correct Answer: 10%

Explanation:


Introduction / Context:
When SP for some count equals CP for a different count, the profit% can be derived by comparing SP per unit with CP per unit.


Given Data / Assumptions:

  • 20 * SP_per_unit = 22 * CP_per_unit


Concept / Approach:
Rearranging gives SP_per_unit / CP_per_unit = 22/20 = 1.10, which means SP is 10% above CP ⇒ 10% profit.


Step-by-Step Solution:

SP_unit = (22/20) * CP_unit = 1.10 * CP_unitProfit% = (SP_unit − CP_unit)/CP_unit * 100 = (0.10)*100 = 10%


Verification / Alternative check:
Assume CP_unit = ₹ 100 ⇒ SP_unit = ₹ 110 ⇒ For 20 units SP = ₹ 2200 = 22 * 100 = cost of 22 units, consistent.


Why Other Options Are Wrong:
12%, 11%, 9%, and 8% do not match the strict ratio 22/20 = 1.10.


Common Pitfalls:
Taking difference 22 − 20 = 2 then reporting 2% instead of using the ratio; percentages must be relative to CP.


Final Answer:
10%

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