When a Increases by 18% then B increases by 16% and when B increases by 18% a is increased from 32 to 48 C must therefore increase from 80 to?

To calculate percentage increases and decreases, we use Percentage multipliers. Percentage multipliers allow us to calculate percentage increases and percentage decreases very quickly, with one single multiplication.

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Tutorial: Percentage Increases & Decreases - Percentage Multipliers

By the end of this section we'll know how to find percentage multipliers as well as calculate any percentage increase, or decrease, such as:

Increasing $48$ by $35\%$ or Decreasing $220$ by $40\%$ We start by watching the following tutorial.

Tutorial: Percentage Increases & Decreases - Percentage Multipliers

In the following tutorial we learn how to calculate percentage increases and decreases using percentage multipliers.

The method shown in the tutorial is summarized here in three steps.

To increase, or decrease a number $N$, by a percentage $X\% $ we multiply $N$ by a percentage multiplier (often just called multiplier).

We can calculate any percentage increase, or decrease, in three steps:

Step 1: write $X\% $ in decimal form. Remember, this is done by moving the number $X$ back two decimal places.
Example: $5\% = 0.05$, $12\% = 0.12$, ... .
Step 2: Calculate the percentage multiplier by adding, or subtracting, the decimal found in step 1 to, or from, $1$
- For percentage increases: add the decimal to $1$.
- For percentage decreases: subtract the decimal from $1$.
Step 3: multiply the number $N$ by the multiplier, found in Step 2.

Increase $80$ kg by $23\% $.

Solution

We follow our three-step method:

Step 1: we write $23\%$ in decimal form: \[23\% = 0.23\]
Step 2: we find the multiplier. Since we're increasing by $23\%$, we add $0.23$ to $1$: \[1 + 0.23 = 1.23\]
Step 3: we multiply $80$ by the multiplier $1.23$: \[80 \times 1.23 = 98.4\] So $80$kg increased by $23\%$ is $98.4$ kg.

Decrease $\$ \ 120$ by $19\% $.

Solution

We follow our three-step method:

Step 1: we write $19\%$ in decimal form: \[19\% = 0.19\]
Step 2: we find the multiplier. Since we're decreasing by $19\%$, we subtract $0.19$ from $1$: \[1 - 0.19 = 0.81 \]
Step 3: we multiply $80$ by the multiplier $0.81$: \[120 \times 0.81 = 97.2\] So $\$ \ 120$ decreased by $19\%$ is $\$ \ 97.20$.

Find the percentage multipliers for each of the following increases and decreases:

Note: this exercise can be downloaded as a worksheet to practice with: Worksheet 1

Using a percentage multiplier, and stating its value, calculate each of the following:

Increase $240$ by $18\%$.

Decrease $820$ by $12\%$.

Increase $150$ by $6\%$.

Decrease $ 550$ by $9\%$.

Increase $70$ by $200\%$

Increase $ 68$ by $37\%$.

Decrease $120$ by $2.5\%$

Decrease $ 98$ by $14\%$.

Increase $640$ by $118\%$

Decrease $ 504$ by $67\%$.

Increase $49$ by $12.7\%$

Decrease $ 82$ by $9.9\%$.

Note: this exercise can be downloaded as a worksheet to practice with: Worksheet 2

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Increased by 18% and then decreased by 16%

A number that is increased by 18% and then decreased by 16% is called sequential percentage calculation or successive percentage calculation. 18 percent minus 16 percent is 2 percent, but you cannot simply take 2 percent of a number to get the correct answer when you want to increase a number by 18 percent and then decrease the result by 16 percent. We created the calculator below, where you can enter any number and we will increase it by 18% and then decrease the result by 16% for you. Do you want to learn how our calculator above works? Below are two methods you can use to increase a number by 18 percent and then decrease the result by 16 percent.
Formula Method This is our favorite method to increase a number by 18 percent and then decrease the result by 16 percent. We simply convert the two percentages into one percentage using this formula: When we enter a = 18 and b = -16 into our formula above and solve it, we get the following:

(18) + (-16) +

2 + (-2.88) = -0.88% Now you know that -0.88% is the same as increasing a number by 18 percent and then decreasing the result by 16 percent. For example, 100 increased by 18% and then decreased by 16% can be calculated by using -0.88% like this:

100 -

= 99.12

Step-by-Step Method This is the most common method used to increase a number by 18 percent and then decrease the result by 16 percent. You literally first increase the number by 18 percent and then decrease the result by 16 percent. Let's use 100 again as an example:

118 -

= 99.12

Sequential Percentage Calculator Need different successive percentage calculations? No problem, please enter it below.

A number is increased by 18% and then decreased by 17%

Here is another sequential percentage calculation that may be of interest.
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