For an article, the ratio of selling price to cost price is 13 : 17. What is the percentage loss incurred on the article?

Introduction / Context:
This is a simple ratio based profit and loss question. Instead of giving actual numerical prices, the question provides the ratio of selling price to cost price, and we must determine whether there is a profit or loss and its percentage. Such questions test understanding of how to interpret price ratios and translate them into profit or loss percentages.

Given Data / Assumptions:

• Ratio of selling price to cost price (SP : CP) is 13 : 17.
• This means SP / CP = 13 / 17.
• Since SP is less than CP, there is a loss.
• We need the loss percentage.

Concept / Approach:
Let cost price be CP and selling price be SP:

• SP / CP = 13 / 17.
• We can assume CP = 17 units and SP = 13 units for convenience.
• Loss = CP - SP = 17 - 13 = 4 units.
• Loss percent = (Loss / CP) * 100.

This approach avoids actual rupee values and works entirely with the ratio numbers, which keeps the calculations simpler.

Step-by-Step Solution:
Given SP : CP = 13 : 17. Assume CP = 17 and SP = 13 (in the same units). Loss = CP - SP = 17 - 13 = 4. Loss percent = (Loss / CP) * 100. Loss percent = (4 / 17) * 100. Compute 4 / 17 ≈ 0.23529. Loss percent ≈ 0.23529 * 100 ≈ 23.529%. Rounded to two decimal places, this is approximately 23.52%.

Verification / Alternative check:
Take an actual numeric example with CP = Rs 17:

• Selling price SP = Rs 13.
• Loss = 17 - 13 = Rs 4.
• Loss percentage = (4 / 17) * 100 ≈ 23.529%.

This is exactly the same as the ratio based calculation and shows that the result does not depend on the actual currency units chosen, only on the ratio of SP to CP.

Why Other Options Are Wrong:
A loss of 27.74%, 18.62%, 19.45% or 13.5% corresponds to different SP : CP ratios, not 13 : 17. Only 23.52% closely matches 4 / 17 * 100 and is therefore correct for the given ratio. Any other value would be mathematically inconsistent with SP / CP = 13 / 17.

Common Pitfalls:
Some learners mistakenly treat the ratio as CP : SP and compute profit instead of loss, or they use SP as the base when calculating percentage loss, which is incorrect since loss percent is always on cost price. Others reduce the ratio incorrectly or miscalculate the fraction 4 / 17. Always identify whether SP is greater or less than CP first and then use the correct base when computing percentages.

Final Answer:
The loss percentage on the article is approximately 23.52%.