Data Sufficiency Analysis

The question asks for the profit percentage. To calculate this, we need to determine the relationship between the Selling Price (SP) and the Cost Price (CP). The formula for profit percent is:

Profit % = ( (SP - CP) / CP ) × 100

Let's analyze the statements to see if we can find the values of SP and CP, or at least a direct ratio between them. Let LP be the List Price.

Evaluating the Statements

Statement I: "5% discount is given on the list price."

• This gives us an equation: SP = LP × (1 - 0.05) → SP = 0.95 × LP.
• This alone is not sufficient as we don't know the LP or CP.

Statement II: "If the discount is not given, 20% profit is gained."

• "If the discount is not given" means the selling price would be the list price (SP = LP).
• This gives us an equation based on profit: (LP - CP) / CP = 0.20 → LP = 1.20 × CP.
• This alone is not sufficient as it describes a hypothetical sale, not the actual one.

Statement III: "The cost price of the articles is Rs. 5,000."

• This gives us: CP = 5000.
• This alone is not sufficient as we don't know the actual SP.

Combining the Statements

Let's see if combining statements provides enough information.

Combining Statement I and Statement II:

• From I, we have: SP = 0.95 × LP
• From II, we have: LP = 1.20 × CP
• We can substitute the expression for LP from the second equation into the first equation:
• SP = 0.95 × (1.20 × CP) → SP = 1.14 × CP
• Now we have a direct relationship between the actual Selling Price and the Cost Price. We can calculate the profit percentage without needing to know the actual monetary values.
• Profit % = ( (1.14 × CP - CP) / CP ) × 100 = (0.14 × CP / CP) × 100 = 14%.
• Since we can find a unique answer, Statements I and II together are sufficient.

Conclusion

Statements I and II together are sufficient to answer the question. Statement III provides the actual cost price, but this information is not necessary to calculate the profit *percentage*. Therefore, the correct answer is "Only I and II".