Percent Decrease Formula

When a value is reduced by a certain percentage over some time, it is referred to as a percentage reduction formula. For instance, a drop in rainfall, a drop in the number of Covid patients, and so on. The percent decrease formula may be used to compute the percent decrease. The percent drop formula will be discussed in this section. Let's look at a few examples of the Percentage reduction formula.

Percent Change

Percent change, or the amount to which something gains or loses value, is defined by the percentage increase and decrease formula. Percent changes are useful for consumers to understand how a value changes over time. Remember that we were supposed to divide by the original value in the procedure above. Another method to remember the procedure is to divide by the old value before subtracting the old value from the new value. Convert the decimal value to a percentage. The percentage increase and decrease formula are represented below.

Percent Change = \[\frac{\left | New \, Value  -  Old\, Value \right |}{Old\, Value}\]*100

What is the Percent Decrease Formula?

The percent decrease gives the decrease in quantity for its starting value. To compute the percentage drop, we must first determine the difference in the data. The percentage decrease formula is used to determine how much a variable's value has decreased. The variable might be population, cost, profit, or something else entirely. Then increase the difference by 100 and divide by the start amount. The percent decrease equation is as follows:

Percent Decrease = \[\frac{\left | Starting \, Value  -  Final\, Value \right |}{Starting\, Value}\]*100

Solved Examples

Ex.1. At a supermarket, a certain item has increased from 64 cents per pound to 86 cents per pound. What is the percent increase in the cost of the item?

Solution:

Percent Change = \[\frac{\left | New \, Value  -  Old\, Value \right |}{Old\, Value}\]*100

Percent Change = \[\frac{\left |86 - 64\right |}{64}\]*100

Percent Change = \[\frac{22}{64}\]*100

Percent Change = 0.34*100

Percent Change = 34%

Hence there was a 34% increase in the cost of the item.

Ex.2. Four feet are cut from a 12-foot board. Find the percent decrease in length?

Solution: 

Percent Change = \[\frac{\left | New \, Value  -  Old\, Value \right |}{Old\, Value}\]*100

Percent Change = \[\frac{\left |12 - 8\right |}{12}\]*100

Percent Change = \[\frac{4}{12}\]*100

Percent Change = 0.33*100

Percent Change = 33.33%

Hence there was a 33.3% decrease in length.

Ex.3. The number 56 is misread as 31. Find the percent decrease by using the percent decrease formula.

Solution:

Here, new value = $ 31 and old value = $ 56

Starting value - Final Value = 56 - 31 = 25

Using the Percent decrease formula, we get

Percent Decrease = \[\frac{\left | Starting \, Value  -  Final\, Value \right |}{Starting\, Value}\]*100

Percent Decrease = \[\frac{25}{26}\]*100

Percent Decrease = 0.4464*100

Percent Decrease = 44.64%

Percent Decrease 45%

Hence the percent decrease of the number is approximately 45%.

Ex.4. An article whose CP is $ 350 was sold for $ 230. Find the percent decrease in the price of the article by using the percent decrease formula.

Solution:

Here, new value = $ 230 and old value = $ 350

Starting value - Final Value = 350 - 230 = 120

Using the Percent decrease formula, we get

Percent Decrease = \[\frac{\left | Starting \, Value  -  Final\, Value \right |}{Starting\, Value}\]*100

Percent Decrease = \[\frac{120}{350}\]*100

Percent Decrease = 0.3428*100

Percent Decrease = 34.28%

Percent Decrease 34%

Hence The percent decrease in the price of the article is 34%