Introduction:
To find out how much percent consumption of tea should be decreased in order to keep the expenditure the same, we need to understand the relationship between price, consumption, and expenditure.

Understanding the problem:
When the price of tea is increased by 10%, the expenditure on tea will increase if the consumption remains the same. On the other hand, if the consumption is decreased, the expenditure can be kept the same despite the price increase.

Calculating the expenditure:
Let's assume the initial price of tea is P and the initial consumption is C. Therefore, the initial expenditure (E) on tea can be calculated as E = P * C.

Impact of price increase:
If the price of tea is increased by 10%, the new price (P') will be P + (P * 10/100) = P + 0.1P = 1.1P.

Calculating the new expenditure:
If the consumption remains the same, the new expenditure (E') can be calculated by substituting the new price (P') in the formula: E' = P' * C = 1.1P * C.

Keeping the expenditure the same:
To keep the expenditure the same, we need to find the new consumption (C') that satisfies the equation E = E'. Substituting the initial expenditure (E = P * C) and the new expenditure (E' = 1.1P * C') in the equation, we get P * C = 1.1P * C'.

Solving for new consumption:
By canceling out the common terms, we have C = 1.1C'. Dividing both sides by 1.1, we get C' = C/1.1.

Calculating the percent decrease in consumption:
To find the percent decrease in consumption, we can use the formula: Percent decrease = ((Initial value - Final value) / Initial value) * 100. Substituting the initial consumption (C) and the new consumption (C') in the formula, we get Percent decrease = ((C - C') / C) * 100 = ((C - C/1.1) / C) * 100 = ((0.1C) / C) * 100 = 10%.

Conclusion:
To keep the expenditure on tea the same when the price is increased by 10%, the consumption of tea should be decreased by 10%. This means the consumption needs to be reduced by 10% in order to compensate for the price increase and maintain the same expenditure.

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