What was the percent profit or loss made by selling an article for ₹ 24,000? I. The ratio of selling price to cost price is 5 : 3. II. The difference between cost price and selling price is ₹ 9,600 (direction not stated).

Introduction / Context:
This is a data-sufficiency problem about profit/loss percentage given a fixed selling price of ₹ 24,000. We must decide which statement(s) give enough information to compute the percentage unambiguously, not actually compute it unless needed to justify sufficiency.

Given Data / Assumptions:

• SP = ₹ 24,000 (fixed).
• Statement I: SP : CP = 5 : 3.
• Statement II: |CP − SP| = ₹ 9,600 (direction unspecified).

Concept / Approach:
Profit% = (SP − CP) / CP * 100; Loss% = (CP − SP) / CP * 100. A ratio SP:CP or explicit CP uniquely determines the percentage. A mere “difference” without direction may yield two possible CP values.

Step-by-Step Solution:
Using I: SP:CP = 5:3 ⇒ Profit% = (5−3)/3 * 100 = 200/3 ≈ 66.67% (unique). Sufficient.Using II alone: |CP − 24,000| = 9,600 ⇒ CP = 14,400 (profit) or 33,600 (loss). Two different percentages (≈66.67% profit or ≈28.57% loss). Insufficient.Combining does not change the fact that I alone already suffices.

Why Other Options Are Wrong:
II alone is ambiguous; “either” is false since II fails; “both necessary” is false since I alone works; “even both not sufficient” is false.

Common Pitfalls:
Interpreting “difference” as signed; here it is stated without direction, producing two CP candidates.

Final Answer:
Statement I alone is sufficient; Statement II alone is not.