Percent profit — which statements suffice? I. Labelled price (LP) of each article is 130% of cost price (CP). II. Cost price (CP) of each article is $550. III. Discount offered is 10% on LP.

Introduction / Context:
This is a Data Sufficiency (DS) item about profit percent. We must identify which statements provide enough information to determine the percentage profit earned by the shopkeeper, not necessarily the numeric selling price.

Given Data / Assumptions:

• I: LP = 130% of CP ⇒ LP = 1.30 * CP.
• II: CP = $550 (a specific value).
• III: Discount = 10% on LP ⇒ SP = 0.90 * LP.
• Profit% = ((SP − CP) / CP) * 100.

Concept / Approach:
If we can express SP in terms of CP alone, the profit percent becomes independent of the absolute CP. Using I and III together gives SP = 0.90 * (1.30 * CP) = 1.17 * CP, so profit% = (1.17 − 1)*100 = 17% without knowing CP numerically.

Step-by-Step Solution:

Verification / Alternative check:
Even if CP were $550, the profit percent remains 17%. Statement II would only produce an SP dollar value, not needed for the percent.

Why Other Options Are Wrong:

• Only I: Discount unknown ⇒ cannot get SP.
• Only III: Relationship between LP and CP unknown.
• Only II: Neither LP nor discount rate given.
• All three: Overkill; I + III suffice.

Common Pitfalls:
Thinking percent profit needs CP numerically; it does not when the pricing chain is fully proportional.

Final Answer:
Only I and III