Percentage decrease is the measure to identify how much a variable has lost its value. The variable can either be population, cost, profit, etc. Here, the percent decrease formula is given along with solved examples for better understanding.

Percentage decrease can be obtained by simply dividing the decreased value by the original value and multiplying that with 100.

therefore\(\, Percent\, Decrease\, Formula\, = \frac{Decreased\, Value}{Original\, Value}\times 100\)

*Here, Decreased Value = Original Value – New Value*

This percent decrease formula can help to solve several questions. Some important questions involving this formula are given below.

**Example 1:**

*A shopkeeper used to sell a pair of pens for Rs. 25. He then reduced the price of the same pair of pens to Rs. 21. Calculate the percentage decrease in the cost.*

**Solution:**

In this question, the decrease amount is = Rs. (25-21) = Rs. 4

Now, percentage decrease = (4/ 25) × 100 = 16%.

**Example 2:**

*A fruit seller used to sell bananas for Rs. 40 per dozen. Now he reduced the cost of a dozen bananas by 10%. What is the price of a dozen bananas now?*

**Solution:**

Let the new value for a dozen bananas be Rs. x.

Now, decrease value = Rs. (40 – x)

According to percent decrease formula,

*%D = (Decrease/ Old value) × 100*

It is given that %D = 10. So, putting the values in the equation, the following is obtained.

\(\frac{10}{100}=\frac{40-x}{40}\)

=> 40 – x = 4

=> x = 36

So, the new price of a dozen of bananas is Rs. 36.

**Example 3:**

*A membership card of a club was reduced by 20% and costs Rs. 550 now. What was the original price of the membership card before its cost reduced?*

**Solution:**

Let the original cost be Rs. x

As the new cost is Rs. 550,

Decrease = Rs. (x – 550)

%D = decrease/ original × 100

therefore\( \frac{x-550}{x}=\frac{20}{100}\)

So, 5x – 2750 = x

=> x = 687.5

Hence, the original price was Rs. 687.5