Relating CP and SP percentages What percent of the selling price equals 34% of the cost price if gross profit is 26% of the selling price?

Introduction / Context:
We are asked to express a fraction of cost price as a percentage of selling price, given a profit relation to selling price. This requires expressing CP in terms of SP and then scaling the specified fraction.

Given Data / Assumptions:

• Gross profit = 26% of SP ⇒ SP - CP = 0.26 SP.
• Hence CP = 0.74 SP.
• We need 34% of CP as a percent of SP.

Concept / Approach:
Compute 34% of CP and then divide by SP to convert it to a percentage of SP.

Step-by-Step Solution:
CP = 0.74 SP.34% of CP = 0.34 × 0.74 SP = 0.2516 SP.Therefore, as a percent of SP: 0.2516 × 100 = 25.16.

Verification / Alternative check:
Using fractions: CP/SP = 74/100, then 34% of CP = (34/100) × (74/100) SP = 2516/10000 SP = 25.16% of SP.

Why Other Options Are Wrong:
17.16 and 26.84 arise from mixing bases; 74.00 and 88.40 are unrelated to the computed chain.

Common Pitfalls:
Accidentally using profit% on CP or applying 34% directly to SP rather than CP.

Final Answer:
25.16