Percentages
A sale of 50 % off plus an extra 20 % off. Is that a 70 % discount? A price with 21 % VAT already included. How can you tell how much it cost without VAT? Percentages are everywhere, and mastering them stops you from being fooled by an advert or an invoice.
Revision: calculating a percentage
Calculate mentally: a) $25\%$ of $240$. b) $10\%$ of $380$. c) $50\%$ of $96$. d) $75\%$ of $800$.
Calculate mentally:
a) $25\%$ of $240$.
b) $10\%$ of $380$.
c) $50\%$ of $96$.
d) $75\%$ of $800$.
A handball team has won $12$ of the $20$ matches it has played. What is its win percentage so far?
A handball team has won $12$ of the $20$ matches it has played. What is its win percentage so far?
Increases, discounts and chained percentages
Express each percentage as a decimal and as an irreducible fraction: a) $35\%$ b) $4\%$ c) $120\%$
Express each percentage as a decimal and as an irreducible fraction:
a) $35\%$
b) $4\%$
c) $120\%$
A comic shop offers the second item at $50\%$ of its price. If a volume of manga costs $9,95\text{ €}$: a) How much do two volumes cost? b) What total percentage…
A comic shop offers the second item at $50\%$ of its price. If a volume of manga costs $9,95\text{ €}$:
a) How much do two volumes cost?
b) What total percentage discount is applied on the purchase of the two volumes?
A sports shop advertises: "Sale: $50\%$ off plus an extra $20\%$ off: a total discount of $70\%$!". A pair of trainers at the shop costs $120\text{ €}$. Explain the…
A sports shop advertises: "Sale: $50\%$ off plus an extra $20\%$ off: a total discount of $70\%$!". A pair of trainers at the shop costs $120\text{ €}$. Explain the error in the advert, calculate the actual percentage discount applied and the correct final price of the trainers.
Undoing a percentage: VAT and the base price
When you know the final price with a percentage already included, to undo it you divide by the multiplier instead of multiplying.
Lucía bought a pair of headphones on a website for $96,80\text{ €}$. This price already included a discount of $20\%$ on the base price and a $21\%$ VAT rate applied…
Lucía bought a pair of headphones on a website for $96,80\text{ €}$. 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?
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…
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?
Recovering a decrease: percentages are not symmetrical
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…
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…
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.
Back to the start: A discount of 50 % plus an extra 20 % is equivalent to paying $0{,}50 \cdot 0{,}80 = 0{,}40$ (a real reduction of 60 %, not 70 %); and to find the price without VAT, divide the final price by $1{,}21$.