A rectangle’s length increases by 60%. By what percentage must its width decrease to keep the area unchanged?

Introduction / Context:
Area of a rectangle is length * width. If one dimension increases, the other must adjust inversely to maintain constant area. This inverse-percentage relation is a common aptitude theme involving scale factors and reciprocal adjustments.

Given Data / Assumptions:
Length factor = 1.60; area must remain the same.

Concept / Approach:
If A = L * W remains constant and L is multiplied by 1.6, then W must be multiplied by 1/1.6 to offset this change. Compute 1/1.6 and convert the resulting factor to a percentage decrease relative to the original width.

Step-by-Step Solution:

Verification / Alternative check:
Let original width be 100 units. New width = 62.5. New length = 160 (if original was 100). New area = 160 * 62.5 = 10,000, matching the original 100 * 100.

Why Other Options Are Wrong:
60% or 75% ignore reciprocal scaling. “None of these” does not apply because 37.5% is exact. 25% is an under-correction.

Common Pitfalls:
Subtracting 60% from 100% to get 40% and misinterpreting as remaining width rather than the correct reciprocal. Always use the inverse factor for constant-product constraints.

Final Answer:
37.5%