Percentage Change

The percentage change formula is used to determine the percentage change in values when there is a change in values. The percentage change formula can be used to figure out how much discounts have changed, how much product prices have changed, or how much income has changed. It is the difference in new value compared to the old value, presented as a percentage. The difference in value is multiplied by 100 after being divided by the original value.

Per cent change, or the amount to which something gains or loses value, is defined by the percentage increase and decrease formula. Per cent 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.

Percentage Change = \[\frac{\left |  \textrm{New value-Old value} \right |}{\left | \text{Old value} \right |}\times 100\]

Percentage Increase Formula

Many times in basic mathematics, we must compute the percentage value of a word.

It is necessary to present the reference value as a ratio using 100 as the standard basis. For example, if we want to present a student's grades in his final grade, we must compute the percentage marks. As can be seen, the percentage number is necessary for obtaining a comparative analysis of particular data.

The formula for percentage increase is the ratio of the increased value to the original value multiplied by 100. It's calculated in percentages. When the worth of anything increases, the percentage increase as well.

The Percentage Increase Formula is given as,

Percentage Increase Formula  =\[\frac{\text{Increase Value}}{\text{Original vale}}\times100\]

Percentage Decrease Formula

The per cent 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 percentage decrease formula is as follows:

Percentage Decrease Formula  =\[ \frac{\left | \text{Starting Value - Final Value }\right |}{\left | \text{Starting Value} \right |}\times 100\]

Percentage Difference Formula

The absolute value of the difference between two quantities, divided by the average of those two values, multiplied by 100 per cent, is the percentage difference between two values.

The percentage difference formula is as follows:

Percentage difference formula = \[\frac{(\text{difference between the two values})}{(\text{the average mean of the values})}\times100 \]

Percentage difference formula =\[\frac{(\text{Second Value-First Value} )}{(\text{Second Value+First Value })/2}\times100 \]

Solved Examples 

Ex.1. At a super mall, a certain item has increased from 71 cents per pound to 98 cents per pound. Calculate growth percentage in the cost of the item?

Solution:

Percentage Change = \[\frac{\left |  \textrm{New value-Old value} \right |}{\left | \text{Old value} \right |}\times 100\]

Percent Change = \[\frac{\left | 98- 71 \right |}{71}\times 100\]

Percent Change = \[\frac{27}{71}\times 100\]

Percent Change = \[0.38\times 100\]

Percent Change = 38%

Hence there was a 38% increase in the cost of the item.

Ex.2. Calculate the percentage increase in the rent of the house if in January it was Rs. 12,000 and in March, it is Rs. 16,000?

Solution:

We can see that there is an increase in the amount of rent.

Here, Increased value = 16000 – 12000 = 4000

Original Value = 12000

Here, formula to calculate percentage increase

Percentage Increase Formula  =\[\frac{\text{Increase Value}}{\text{Original vale}}\times100\]

=\[\frac{4000}{12000}\times 100\]

= \[0.33 \times 100\]

=  33%

Hence, there is a 33% increase in the amount of rent.

Ex.3. The price of a kilogram of rice went from 18 to 22.5, calculate percentage difference?

Solution: 

The old value of sugar = $ 18

• New value = $22.5

• Now apply the percentage change formula;

• Percentage difference formula = \[\frac{(\text{Second Value - First Value} )}{\frac{(\text{Second Value+First Value })}{2}}\times 100\]

Percentage difference formula = \[\frac{(\text{Second Value - First Value} )}{\frac{(\text{Second Value+First Value })}{2}}\times 100\]

=\[\frac{(22.5-18)}{\frac{(22.5+18)}{2}}\times 100\]

=\[\frac{4.5}{\frac{(30.5)}{2}}\times 100\]

=\[\frac{4.5}{15.25}\times100\]

=\[0.295\times 100\]

= 29.5%

Ex.4. A book whose CP is ＄150 was sold for ＄ 110. Find the percentage decrease in the price of the book by using the percentage decrease formula.

Solution:

Here, new value = ＄ 110 and old value = ＄150

Starting value - Final Value = 150 - 110 = 40

Here is the percentage decrease formula for calculating percentage reduction.

Percentage Decrease  =\[ \frac{\left | \text{Starting Value-Final Value }\right |}{\left | \text{Starting Value} \right |}\times 100\]

Percentage Decrease  = \[\frac{40}{150}\times100\]

Percentage Decrease  = \[0.2667\times100\]

Percentage Decrease  = 26.67%

Percentage Decrease  ∼ 27%

Hence The percentage decrease in the price of the article is 27%