If the price of sugar increases by 20%, by what percentage should a 
household reduce its consumption of sugar so that the budget remains the 
same ?

If the price of sugar increases by 20%, we need to find the percentage by which the household should reduce its sugar consumption to keep their total expenditure on sugar unchanged.

Let the initial price of sugar be \( P \) and the initial consumption be \( C \). Therefore, the initial expenditure is:

\[
\text{Initial Expenditure} = P \times C
\]

Now, the price increases by 20%, so the new price becomes \( 1.2P \). Let the new consumption be \( C' \), and the expenditure must remain the same. Thus, we set the new expenditure equal to the initial expenditure:

\[
1.2P \times C' = P \times C
\]

To find \( C' \), divide both sides by \( 1.2P \):

\[
C' = \frac{P \times C}{1.2P} = \frac{C}{1.2}
\]

Now, \( C' = \frac{C}{1.2} \) implies that the new consumption is \(\frac{1}{1.2}\) of the original consumption. In terms of percentage, this is approximately:

\[
C' \approx 0.833C
\]

This means the household should reduce its consumption by:

\[
1 - 0.833 = 0.167 = 16.7\%
\]

Thus, the household should reduce its sugar consumption by approximately **16.7%** to keep the budget unchanged.

Would you like more details or further explanations? Here are five related questions you might find interesting:

1. What happens if the price increases by 50% instead of 20%?
2. How would this change if the household has a fixed budget for sugar?
3. What if the price decreases by 10%, how much should consumption increase to maintain the same budget?
4. Can this same principle be applied to other goods? How?
5. How do households adjust when multiple prices change at once?

**Tip:** When dealing with percentage changes in price and consumption, think of the product of the two as your fixed budget.

If the price of sugar increases by 20%, by what percentage should a household reduce its consumption of sugar so that the budget remains the same?

Find out how much a household should reduce its sugar consumption to maintain the same budget after a 20% price increase. This problem involves percentage change, proportions, and simple algebra. Perfect for students in Grades 9-11.

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