P is six times as large as q (P = 6q). By what percentage is q less than P?

Introduction / Context: “q is less than P by what percent” requires using P as the base for the percentage comparison. With P = 6q, compute the relative shortfall of q from P and express it as a fraction of P.

Given Data / Assumptions:

• P = 6q, with q > 0.
• Percent less than P is (P − q)/P * 100%.

Concept / Approach: Substitute P = 6q; then the numerator becomes 5q and the denominator 6q. The q cancels, leaving a pure ratio that converts directly to a percentage.

Step-by-Step Solution:

Verification / Alternative check: Choose q = 1 ⇒ P = 6. q is 5 less than P; 5 is 5/6 of 6 ⇒ 83 1/3%.

Why Other Options Are Wrong: 16 2/3% is the complement (q as a percent of P), not the deficit; 60% and 90% ignore the correct base.

Common Pitfalls: Using q as the base and computing (P − q)/q, which would answer “how much greater is P than q,” a different question.

Final Answer: 83 1/3