x is six times as large as y. The percentage by which y is less than x, is :

Concept: When a larger quantity B exceeds a smaller quantity A, the percentage by which A is less than B is calculated using B as the base: Percentage = ((B − A) / B) × 100.

1. Let y = 1 unit; since x is six times as large as y, x = 6 × 1 = 6.

2. Find the difference between the two quantities: x − y = 6 − 1 = 5.

3. Apply the "less than" formula with x as the base (the comparison is "y is less than x"): Percentage = ((x − y) / x) × 100 = (5 / 6) × 100.

4. Simplify: (5 / 6) × 100 = 500 / 6 = 83 1/3.

Cross-check: If y is 83 1/3% less than x, then y should equal x × (1 − 5/6) = x × (1/6). Since x = 6y, x × (1/6) = 6y × (1/6) = y, which matches the given relation — confirming the result.

Result: y is less than x by 83 1/3%.