.The price of sugar has been increased by 40%. By how much percent must this new price be decreased to retain its former price.

Let the original price of sugar be \( P \).

After a 40% increase, the new price becomes:
\[
P_{\text{new}} = P + 0.40P = 1.40P
\]

Now, let \( x \% \) be the percentage by which the new price must be decreased to return to the original price. The new price after a decrease of \( x \% \) will be:
\[
(1 - \frac{x}{100}) \times 1.40P
\]

To retain the original price, this must equal \( P \):
\[
(1 - \frac{x}{100}) \times 1.40P = P
\]

Dividing both sides by \( P \):
\[
(1 - \frac{x}{100}) \times 1.40 = 1
\]

Simplifying:
\[
1 - \frac{x}{100} = \frac{1}{1.40}
\]

\[
1 - \frac{x}{100} = 0.7143
\]

\[
\frac{x}{100} = 1 - 0.7143 = 0.2857
\]

\[
x = 28.57\%
\]

Thus, the new price must be decreased by approximately **28.57%** to retain its original price.

Would you like further clarification on this? Here are 5 related questions:

1. If the price had increased by 50%, what would be the required percentage decrease?
2. How would you calculate the percentage decrease if the original increase was only 20%?
3. Can this method be applied to any type of price adjustment problem?
4. How would this calculation change if instead of percentages, a fixed amount was added or removed from the price?
5. What happens if the price was first decreased and then increased?

**Tip:** To revert an increase, the decrease is always calculated on the new price, making the percentage decrease smaller than the increase percentage.

The price of sugar has been increased by 40%. By how much percent must this new price be decreased to retain its former price?

This page provides a step-by-step solution to calculate the percentage decrease needed to revert a 40% price increase to the original value. Learn key concepts in percentage changes and algebra, suitable for students in Grades 8-10.

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