The price of rice rises by 60%. By what exact percentage should the new price be reduced to restore the original price?

Introduction / Context:
This is a reverse change problem. After an increase of 60%, the compensating decrease to return to the original price is found relative to the increased base, not the original base, so it is less than 60% but not equal to 60% either.

Given Data / Assumptions:

• Initial price = P.
• Increased price = P * 1.60.
• We need reduction r such that (1 − r) * 1.60P = P.

Concept / Approach:
Set up the equation and solve for r: (1 − r) = 1 / 1.60 = 0.625. Therefore r = 1 − 0.625 = 0.375 = 37.5%. This is the general reverse-percentage formula: required reduction r = (increase%) / (100% + increase%) * 100%.

Step-by-Step Solution:

Verification / Alternative check:
Let P = 100. After a 60% rise → 160. Reduce by 37.5%: 160 * (1 − 0.375) = 160 * 0.625 = 100, restored exactly.

Why Other Options Are Wrong:

• 33 1/3% and 40% and 45%: Do not satisfy (1 − r)*1.6 = 1 when tested.

Common Pitfalls:
Assuming the same 60% decrease would undo the increase; reverse changes are based on the new base.

Final Answer: