If a 10% loss is made on the selling price of an article, what will be the corresponding rate of loss on the cost price?

Introduction / Context:
This question tests the ability to switch between loss defined as a percentage of selling price and loss defined as a percentage of cost price. Usually in profit and loss questions, percentages are given with respect to cost price, but here the loss is specified as a fraction of the selling price. Converting between these two bases is a useful skill for percentage arithmetic in aptitude exams.

Given Data / Assumptions:

• Loss is 10% of the selling price (SP).
• We have to find loss percentage with respect to cost price (CP).
• Let selling price be S units.
• Loss amount = 10% of S = 0.10S.

Concept / Approach:
Loss is the difference between cost price and selling price. If loss is given as a fraction of selling price, we can express cost price as selling price plus this loss. Then loss percentage on cost price is calculated as (Loss / Cost price) * 100. The key is to express both cost price and loss in terms of the same variable, here S, and then form the required ratio.

Step-by-Step Solution:
Step 1: Let selling price S be some positive value (for example S units).Step 2: Given that loss is 10% of S, so Loss = 0.10S.Step 3: Since loss = CP - SP, we have CP = SP + Loss = S + 0.10S = 1.10S.Step 4: Now express loss percentage on cost price: Loss% = (Loss / CP) * 100.Step 5: Substitute: Loss% = (0.10S / 1.10S) * 100.Step 6: Simplify the ratio: 0.10S / 1.10S = 10 / 110 = 1 / 11.Step 7: Therefore Loss% = (1 / 11) * 100 = 100 / 11%.Step 8: 100 / 11 = 9 1/11% approximately 9.09%.

Verification / Alternative check:
Take a simple numerical value for S, such as S = 100. Then loss = 10% of 100 = 10. Thus CP = S + Loss = 100 + 10 = 110. Loss percentage with respect to cost price is Loss / CP * 100 = 10 / 110 * 100 = 100 / 11% = 9 1/11%. This exactly matches the algebraic derivation, confirming that the conversion is correct and that the loss percentage on cost price is slightly below 10%.

Why Other Options Are Wrong:
Option A (11 1/9%) and option D (11%) are both greater than 10%, which cannot happen when loss is defined as 10% of selling price because cost price is larger than selling price, making the percentage on cost lower. Option C (10%) simply repeats the given loss percentage on selling price and ignores the change of base to cost price. Only option B correctly translates the 10% loss on selling price into a 9 1/11% loss on cost price.

Common Pitfalls:
Many students mistakenly assume that the loss percentage remains the same when switching from selling price to cost price as base. Others invert the relationship and end up with a higher percentage like 11% or more. Always remember that when CP is greater than SP, a given loss expressed as a percentage of the smaller value (SP) will convert into a smaller percentage when expressed relative to the larger value (CP). Working through the algebra carefully prevents such base confusion.

Final Answer:
The rate of loss on the cost price is 9 1/11%.