If an article is sold at a loss of 15%, what is the ratio of its cost price to its selling price?

Introduction / Context:
This is a straightforward profit and loss ratio question. When an article is sold at a loss, its selling price is lower than its cost price. Expressing the relationship between cost price and selling price as a ratio is a common aptitude exercise and helps reinforce the meaning of percentage loss.

Given Data / Assumptions:
- Loss percentage on the article = 15%. - Cost price is denoted by C. - Selling price is denoted by S. - We are asked for the ratio C : S.

Concept / Approach:
If an article is sold at a loss of L%, then selling price is (100 - L)% of cost price. Here L = 15, so:
S = C * (100 - 15) / 100 = C * 85 / 100. From this relation, we can form the ratio C : S by treating C as 100 units and S as 85 units, and then simplifying the ratio.

Step-by-Step Solution:
Step 1: Assume cost price C = 100 units for easy calculation. Step 2: Loss percent is 15%, so loss amount = 15 units. Step 3: Selling price S = C - loss = 100 - 15 = 85 units. Step 4: Ratio C : S = 100 : 85. Step 5: Simplify by dividing both terms by 5: 100 / 5 = 20 and 85 / 5 = 17. Step 6: Therefore, the required ratio is 20 : 17.

Verification / Alternative check:
Take a real example. Let cost price be Rs 200. A loss of 15% means loss = 15% of 200 = 30. So selling price S = 170. Ratio C : S = 200 : 170 = 20 : 17 after dividing by 10, which matches the earlier result. Hence the ratio is correct.

Why Other Options Are Wrong:
Option 17:20 reverses the correct ratio and would imply selling price is higher than cost price, which is inconsistent with a loss. Options 23:15 and 15:23 bear no direct relation to the 15% loss and do not match when computed for standard values of cost and selling prices.

Common Pitfalls:
A common mistake is to take cost price as 85 and selling price as 100, confusing loss with profit, or forgetting that loss reduces the price. Another error is to simplify the 100:85 ratio incorrectly. Always interpret a loss percentage as a reduction from cost price, not an increase.

Final Answer:
The ratio of cost price to selling price is 20 : 17.