Problem Analysis:
Let's assume the initial price of sugar is P and the initial consumption is C. After the price is increased by 10%, the new price of sugar will be 1.1P. We need to find the percentage reduction in consumption that will result in the same expenditure.

Solution:
To solve this problem, we can start by considering the initial expenditure and the new expenditure after the price increase.

Initial expenditure = P * C
New expenditure = (1.1P) * X (where X is the reduced consumption)

We know that the initial expenditure and the new expenditure should be the same. Therefore, we can set up the equation:

P * C = (1.1P) * X

Solving for X:
Let's solve the equation for X to find the reduced consumption.

P * C = (1.1P) * X

Dividing both sides by P:

C = 1.1X

Dividing both sides by 1.1:

C / 1.1 = X

Therefore, the reduced consumption is C / 1.1.

Calculating the reduction in percentage:
To find the reduction in percentage, we need to calculate the difference between the initial consumption and the reduced consumption, and then express it as a percentage of the initial consumption.

Reduction in consumption = C - (C / 1.1)
= C - C/1.1
= C(1 - 1/1.1)
= C(0.1/1.1)
= 0.1C/1.1

Percentage reduction = (Reduction in consumption / Initial consumption) * 100
= (0.1C/1.1 / C) * 100
= (0.1/1.1) * 100
= 9.09%

Therefore, the consumption should be reduced by 9.09% in order to maintain the same expenditure.

Conclusion:
If the price of sugar is increased by 10%, the consumption should be reduced by 9.09% to maintain the same expenditure.