Calculations with percentages
A computer costs 847 € with VAT already included and, on top of that, has a 30 % discount applied to the original price. What was the real price, without discount or taxes? Questions like this are an everyday part of invoices, sale adverts and stock market reports. The tool is always the same: the multiplier.
The multiplier
A forest has lost $15\%$ of its trees due to a wildfire. If forestry officials have counted $360$ burnt trees, how many trees did the forest have before the fire?
A forest has lost $15\%$ of its trees due to a wildfire. If forestry officials have counted $360$ burnt trees, how many trees did the forest have before the fire?
A family pays $85$ € per month for their broadband and TV package. If the telecoms provider informs them that next month there will be a price increase of $4\%$ due to…
A family pays $85$ € per month for their broadband and TV package. If the telecoms provider informs them that next month there will be a price increase of $4\%$ due to tariff updates, how much will they pay per month from now on?
A pair of trainers with a tag price of $120$ € is discounted by $35\%$ for the end-of-season sale. Calculate the final price to be paid at the till.
A pair of trainers with a tag price of $120$ € is discounted by $35\%$ for the end-of-season sale. Calculate the final price to be paid at the till.
Reversing a percentage: when you know the final amount
If you know the quantity after the percentage has been applied and you are looking for the original, divide by the multiplier instead of multiplying.
After applying a salary increase of $6\%$ agreed in the collective agreement, a worker's net monthly salary is $1643$ €. What was her salary before the pay rise was…
After applying a salary increase of $6\%$ agreed in the collective agreement, a worker's net monthly salary is $1643$ €. What was her salary before the pay rise was applied?
I paid $34$ € for a digital video game that was discounted by $15\%$ during a special promotion. What was the original price of the video game before the discount?
I paid $34$ € for a digital video game that was discounted by $15\%$ during a special promotion. What was the original price of the video game before the discount?
Successive percentages: VAT, discounts and surcharges together
An appliance shop applies a discount of $20\%$ to a high-end television with an initial price of $650$ €. At the till, you present your VIP loyalty card, which gives you…
An appliance shop applies a discount of $20\%$ to a high-end television with an initial price of $650$ €. At the till, you present your VIP loyalty card, which gives you an additional discount of $10\%$ on the already reduced price. Calculate the final price you will pay for the television and determine the single percentage discount equivalent to these two successive reductions.
The value of some stock market shares experienced a rise of $15\%$ during January and subsequently suffered a drop of $12\%$ during February due to market instability.…
The value of some stock market shares experienced a rise of $15\%$ during January and subsequently suffered a drop of $12\%$ during February due to market instability. What was the overall percentage change over the two-month period? Have the shares gained or lost value compared to the start of the year?
A latest-generation laptop costs $847$ € with $21\%$ VAT included. If the shop advertises that all its products have a discount of $30\%$ off the original price (before…
A latest-generation laptop costs $847$ € with $21\%$ VAT included. If the shop advertises that all its products have a discount of $30\%$ off the original price (before tax is applied), what was the original price of the laptop without discount and excluding VAT?
Percentages in areas and mixtures
When a quantity depends on another one squared (an area) or cubed (a volume), its percentage change is not the same as that of the side.
If the side length of a square is increased by $25\%$, by what percentage will its total area increase compared to the original area?
If the side length of a square is increased by $25\%$, by what percentage will its total area increase compared to the original area?
In a winery, $40$ litres of wine with an alcohol content of $12\%$ are mixed with $60$ litres of another wine with an alcohol content of $15\%$. What is the alcohol…
In a winery, $40$ litres of wine with an alcohol content of $12\%$ are mixed with $60$ litres of another wine with an alcohol content of $15\%$. What is the alcohol percentage of the resulting mixture?
When designing a new cylindrical soft drink container, the packaging department decides to increase the base radius by $20\%$ and decrease the height by $15\%$ relative…
When designing a new cylindrical soft drink container, the packaging department decides to increase the base radius by $20\%$ and decrease the height by $15\%$ relative to the dimensions of the original container. What is the exact percentage change in the volume of the new container compared to the old one? State whether it is an increase or a decrease.