Price drop with constant expenditure: If the price of tea decreases by 6%, by what percent must consumption increase to keep total spending unchanged?

Introduction / Context:
When price falls, more can be bought for the same money. The increase needed is not simply 6%; it must offset the 6% price drop exactly.

Given Data / Assumptions:

• Price decrease r = 6%.
• Expenditure must remain the same.

Concept / Approach:
If price multiplies by (1 − r), consumption must multiply by 1/(1 − r). Required percentage increase = [1/(1 − r) − 1] * 100% = r/(1 − r) * 100%.

Step-by-Step Solution:

Verification / Alternative check:
Assume initial price 100, quantity 1 ⇒ spend 100. New price 94. New quantity Q requires 94Q = 100 ⇒ Q = 100/94 = 1.063829… ⇒ 6.3829…% increase = 6 18/47%.

Why Other Options Are Wrong:

• 5 16/47%, 6 17/47% are off by small fractions.
• 4 18/67% is unrelated.
• 6% would leave a slight shortfall in expenditure.

Common Pitfalls:
Adding 6% instead of using the inverse factor; exact compensation requires r/(1 − r), not r alone.

Final Answer:
6 18/47%