Percentage Increase and Decrease

$3\%$ is $\frac{3}{100}$ which is equal to $0.03$.

The price of a bag of rice went up from £20 to £35. What is the percentage increase?

Solution

The formula to be used here is the following,

$$\begin{gathered} Increase=Newnumber-Originalnumber \\ \%Increase=\frac{Increase}{Originalnumber}\times 100 \end{gathered}$$

The first thing is to identify the values that are given. The question says that the price went up from $\pounds 20$ to $\pounds 35$. This means that,

$$\begin{gathered} Originalnumber=20 \\ Newnumber=35 \end{gathered}$$

We will first find the increase.

$$\begin{gathered} Increase=Newnumber-Originalnumber \\ Increase=35-20 \\ =15 \end{gathered}$$

We will now find the percentage increase.

$$\begin{gathered} \%Increase=\frac{Increase}{Originalnumber}\times 100 \\ =\frac{15}{20}\times 100 \\ =75\% \end{gathered}$$

This means the price increased by $75\%$.

A bag contains 15 balls. After some time, the number of balls increased to 35. What is the percentage increase?

Solution

From the question, the original number is $15$ and the new number is $35$.

We will first find the increase as shown below.

$$\begin{gathered} Increase=Newnumber-Originalnumber \\ =35-15 \\ =20 \end{gathered}$$

We will now find the percentage increase.

$$\begin{gathered} \%Increase=\frac{Increase}{Originalnumber}\times 100 \\ \%Increase=\frac{20}{15}\times 100 \\ =133.33\% \end{gathered}$$

This means the number of balls increased by $133.33\%$.

Harry had £2000 in his bank account last week but now he has £800. What is the percentage decrease?

Solution

From the question, the original amount or number is $2000$ and the new amount or number is$800$.

We will first find the decrease using the formula below.

$$\begin{gathered} Decrease=Originalnumber-Newnumber \\ =2000-800 \\ =1200 \end{gathered}$$

We will now use the decrease to find the percentage decrease using the formula below.

$$\begin{gathered} \%Decrease=\frac{Decrease}{Originalnumber}\times 100 \\ =\frac{1200}{2000}\times 100 \\ =60\% \end{gathered}$$

This means the money in Harry’s bank account decreased by $60\%$.

A factory went from producing 200 packs of its product to producing 180. What is the percentage decrease?

Solution

The formula to be used is the following,

$$\begin{gathered} Decrease=Originalnumber-Newnumber \\ \%Decrease=\frac{Decrease}{Originalnumber}\times 100 \end{gathered}$$

From the question, the original number is $200$ and the new number is $180$. So we will first find the decrease and then find the percentage decrease as shown below.

$$\begin{gathered} Decrease=Originalnumber-newnumber \\ =200-180 \\ =20 \\ \%Decrease=\frac{Decrease}{Originalnumber}\times 100 \\ =\frac{20}{200}\times 100 \\ =10\% \end{gathered}$$

The percentage decrease is $10\%$.

Increase £80 by 5%.

Solution

The first thing to do here is to find $5\%$ of $\pounds 80$. We will do this by multiplying $5\%$ by $\pounds 80$.

$5\%\times 80=\frac{5}{100}\times 80=4$.

Now, we will add $4$ to $\pounds 80$ since we are looking for an increase. If it were to be a decrease, we would be subtracting.

$\pounds 80+4=\pounds 84$

Therefore, $\pounds 80$ increased by $5\%$ is $\pounds 84$.

The length of a 70 cm wood was decreased by 3%. What is the new length?

Solution

We want to know the new length after $3\%$decrease. To find this we will solve for $3\%$ of the original wood length which is $3\%of70$.

$$\begin{gathered} 3\%\times 70=\frac{3}{100}\times 70 \\ =2.1 \end{gathered}$$

Since we are looking for the decreased length, we will subtract 2.1 from the original length of 70.

$70-2.1=67.9$

The new length of the wood is $67.9cm$.

Over 2 years, it was noticed that the price of petrol went from £199 per liter to £215 per liter. What is the percentage increase over time?

Solution

We are asked to find the percentage increase over time. The time given is 2 years. Following the steps above, the first thing we would do is divide the new number by the original number and subtract 1.

$$\begin{gathered} \frac{Newnumber}{Originalnumber}-1=\frac{215}{199}-1 \\ =0.08 \end{gathered}$$

We will now multiply by $100$.

$0.08\times 100=8$

The last step is to divide by the time given which is $2years$.

$\frac{8}{2}=4\%/year$

Therefore, the percentage increase over time is $4\%/year$.

Within 30 minutes, the amount of water in a drum went from level 30 to level 15. What is the percentage decrease over 30 minutes?

Solution

Let’s use the formula for this. The formula to be used is below.

$\%Changeovertime=\frac{\left[\left(\frac{newnumber}{originalnumber}-1\right)\times 100\right]}{time}$

All we need to do is to insert the values that are given to us. The values given to us are:

$$\begin{gathered} Time=30minutes \\ Originalnumber=30 \\ Newnumber=15 \end{gathered}$$

We will now insert the values in the formula.

$$\begin{gathered} \%Decreaseovertime=\frac{\left[\left(\frac{15}{30}-1\right)\times 100\right]}{30} \\ =\frac{\left[\left(0.5-1\right)\times 100\right]}{30} \\ =-\frac{0.5}{30} \\ =-0.017\%/min \\ =0.017\%/min \end{gathered}$$

Therefore, the percentage decrease over time is $0.017\%/min$

Notice that the negative sign is taken out. If you get a negative value when calculating, it means that there has been a decrease. You should take out the negative sign and say that the quantity or whatever is being measured has decreased by that value.