Exercises: Percentages

Calculate mentally:

a) $25\%$ of $240$.

b) $10\%$ of $380$.

c) $50\%$ of $96$.

d) $75\%$ of $800$.

Look at the grid in the figure, made up of $100$ squares.

a) What percentage of the squares are shaded?

b) What percentage are left unshaded?

Of the $30$ students in a class, $18$ are girls. What percentage of the class are girls? And boys?

A handball team has won $12$ of the $20$ matches it has played. What is its win percentage so far?

A pair of sneakers costing $\$1\,200$ is reduced by $15\%$. How many pesos do you save? How much do you pay?

A pair of headphones costs $\$1\,000$ excluding sales tax. If sales tax is $21\%$, what is the final price?

Express each percentage as a decimal and as an irreducible fraction:

a) $35\%$

b) $4\%$

c) $120\%$

Vera has a monthly data allowance of $12$ GB and has already used $30\%$. How many gigabytes does she have left?

In a village of $2\,500$ inhabitants, $8\%$ are under $15$ years old. How many people under $15$ years old live in the village?

A travelcard costs $\$400$ and is going to go up by $5\%$. What will the new price be?

What percentage does $45$ represent out of $180$?

Calculate:

a) $150\%$ of $60$.

b) $0.5\%$ of $800$.

Complete in your notebook:

a) If you get a $30\%$ discount, you pay ____ $\%$ of the price.

b) If a price goes up by $12\%$, you pay ____ $\%$ of the original price.

c) If you have used $45\%$ of the battery, you have ____ $\%$ left.

In a survey of $400$ young people, $64\%$ state that they do sport every week. How many young people do sport?

Noa had $\$4\,800$ in savings and spent $25\%$ on a gift for her mother. How much money does she have left?

In a nature park with $12\,000$ trees, $35\%$ are pine trees. How many pine trees are there in the park?

A jacket that cost $\$1\,498$ is reduced by $30\%$. How many pesos are discounted? What is the final price?

I paid $\$1\,190$ for a pair of trousers discounted by $15\%$. What was the price before the discount?

A cooking channel increased its followers by $25\%$ in the last year and now has $1\,800$ followers. How many followers did it have a year ago?

The price of a comic has gone from $\$240$ to $\$300$. What percentage has it gone up by?

A basketball player has scored $17$ of the $25$ free throws she took this season. What is her success percentage?

To buy an electric bike, Andrés deposits $\$24\,000$ into an account paying a simple interest rate of $3\%$ per annum for $2$ years. How much interest will he receive? How much money will he have in total at the end?

A stationer's has a "3 for 2" offer (buy three, pay for two) on felt-tip pens that cost $\$4.50$ each. If you buy $3$ felt-tip pens:

a) How much do you pay in total?

b) What percentage discount does the offer represent compared to the price without discount? Round to two decimal places.

A comic shop offers the second item at $50\%$ of its price. If a volume of manga costs $\$199$:

a) How much do two volumes cost?

b) What total percentage discount is applied on the purchase of the two volumes?

A video game that cost $\$1\,200$ went up by $10\%$ during the Christmas campaign, and after the holidays, the new price dropped by $10\%$.

a) What was the price after the increase?

b) What is the price after the drop?

c) Has it returned to the original price? If not, what is the total percentage change?

An online store sells a backpack for $\$1\,900$ excluding sales tax. It applies a discount of $20\%$ and then adds $21\%$ sales tax to the discounted price. What is the final price you pay?

In a survey of $1\,500$ young people, $40\%$ state that they play team sports, and of those, $25\%$ play basketball. How many young people play basketball? What percentage of the total do they represent?

A reservoir with a capacity of $240\ \text{hm}^3$ was at $35\%$ after the summer. Autumn rains have filled it to $58\%$ of its capacity.

a) How many cubic hectometers of water did it hold after the summer?

b) How many cubic hectometers has it gained from the rain?

State whether these statements are true or false, supporting your answers with numerical examples:

a) If a price goes up by $50\%$ and then goes down by $50\%$, it returns to the initial price.

b) Applying two consecutive discounts of $10\%$ is equivalent to a single discount of $19\%$.

c) $5\%$ of an amount is half of $10\%$ of that same amount.

d) If $90\%$ of the students passed an exam, $1$ in every $10$ failed.

The chart shows the comics that a shop sold between Monday and Friday last week.

a) What percentage of the week's sales were made on Friday?

b) By what percentage did sales on Friday increase compared to Monday?

Two gyms have the following offers:

• Gym A: $\$600$ per month, with a $20\%$ discount if you pay for the full year in advance.

• Gym B: $\$500$ per month, plus a one-off joining fee of $\$800$.

a) Calculate how much a full year costs at each gym.

b) Which one would you choose for one year? What if you only want to join for $6$ months (in which case Gym A does not apply the annual discount)? Justify both answers.

A recycling bin collects $800$ kg of packaging. $45\%$ of the weight is plastic and, of that plastic, only $60\%$ can be recycled.

a) How many kilograms of plastic are in the bin?

b) How many kilograms are actually recycled?

c) What percentage of the total bin contents is recycled?

The ticket price for a water park dropped by $20\%$ at the end of the summer. When the next season arrives, the park wants to restore the exact original price. By what percentage must the reduced price increase? Explain why the answer is not $20\%$.

A bookshop's sales fell by $35\%$ in February compared to January. In March, sales recovered to reach the January level again. By what percentage did March sales increase compared to February? Round your answer to two decimal places.

Lucía bought a pair of headphones on a website for $\$1\,936$. This price already included a discount of $20\%$ on the base price and a $21\%$ VAT rate applied after the discount. What was the base price of the headphones, without discount or VAT?

Martín wants to buy a mountain bike and is studying several simple interest deposit options:

a) What principal must he deposit at $4\%$ per annum for $3$ years to get $\$5\,400$ in interest?

b) At what annual percentage rate must he invest $\$50\,000$ for $2$ years to earn $\$4\,000$ in interest?

c) For how long must he keep $\$36\,000$ at $5\%$ per annum to earn $\$7\,200$ in interest?

A sports store advertises: "Sale: $50\%$ off plus an extra $20\%$ off: a total discount of $70\%$!". A pair of sneakers at the store costs $\$2\,400$. Explain the error in the ad, calculate the actual percentage discount applied and the correct final price of the sneakers.

A savings account offers simple interest of $0.4\%$ per month. If you deposit $\$60\,000$:

a) How much interest do you earn each month?

b) How many full months must pass to accumulate $\$3\,600$ in interest?

Nora's family is comparing three cell phone plans:

a) Calculate the cost of a full year for each plan, taking into account the conditions.

b) Nora uses around $45$ GB per month. Which plan suits her best? Justify your answer using your calculations from the previous section.

c) Her father uses $110$ GB per month. Which plan would you recommend to him? How much does he save per year compared to the most expensive one that meets his needs?

Tickets for a music festival have increased by $5\%$ each year for three consecutive years. If three years ago they cost $\$40$:

a) How much do they cost now? Round to the nearest cent.

b) What has been the total percentage increase over the three years? Does it match $15\%$? Give reasons for your answer.

Two shops sell the same rucksack for $\$1\,600$. Shop A reduces it directly by $25\%$. Shop B first applies a discount of $10\%$ and then, on the resulting price, another discount of $15\%$.

a) Calculate the final price of the rucksack in each shop.

b) In which shop is it better to buy it? Explain, showing your calculations, why the two offers are not equivalent.

State whether the following statements are true or false, justifying each answer with a numerical example:

a) An amount cannot increase by more than $100\%$.

b) $200\%$ of an amount is double that amount.

c) If the price of a product goes from $\$1\,000$ to $\$3\,000$, it has increased by $200\%$.

d) It is impossible to reduce a price by $110\%$.

In a secondary school, $360$ students play a federated sport, which represents $37.5\%$ of the total.

a) How many students are there in the school?

b) How many do not play a federated sport?

Here is Alex's family's electricity bill for one month:

• Consumption: $\$1\,248$

• Contracted power: $\$364$

• Electricity tax: $5.11\%$ on the sum of consumption and contracted power

• VAT: $21\%$ on the previous total

a) Calculate the amount of electricity tax, rounding to the nearest cent.

b) Calculate the total amount of the bill.

c) The family installs solar panels and their consumption drops by $40\%$. If the contracted power and taxes are calculated in the same way, what will the total amount of the new bill be?