Arithmetic, Percentages
Percentages are a way of expressing a fraction out of 100. This topic includes converting between percentages, fractions, and decimals, calculating percentage of a quantity, finding percentage increase or decrease, and solving word problems involving discounts, interest, etc.
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Question
Shmuel's salary increased by `20%`, and then decreased by `20%`. Is Shmuel's current salary equal to his initial salary?
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What is more worthwhile?
What is more worthwhile – to receive a discount of `20%`, or to buy a gift voucher worth `120%` of its price?
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Successive Discounts
What is more worthwhile – to receive a `15%` discount and then a `5%` discount, or to first receive a `5%` discount and then a `15%` discount?
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Area and Perimeter
By what percentage will the area of a square increase if its perimeter increases by `10%`?
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Question
Over the course of a year, the price of apples increased twice by `50%` each time, and before Rosh Hashanah, they were discounted by `50%`. What is the new price of a kilogram of apples if, at the beginning of the year, they cost `8` shekels per kilogram?
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Question
Every student in the gymnasium knows at least one of the following two ancient languages: Latin or Ancient Greek. It is known that `85%` of all students know Latin, and `75%` know Greek. What is the percentage of students who know both languages?
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Question
The company "The Diligent Builder" is engaged in stockpiling trees in a magical forest in Canada. A nature protection association called "The Green Avenger" wants to protect the forest and opposes the company's activity. As a result, the company's CEO said the following sentence:
"`99%` of the trees in the forest are maple trees. In the coming year, we are going to cut down only maple trees, and as a result, the percentage of maple trees in the forest in a year will become `98%`."
What percentage of the trees in the forest do the Diligent Builders intend to cut down?
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The Orange Path
In the illustration, there is an orange path surrounding a blue square. The area of the path is 44% of the area of the square.
What is the width of the orange path as a percentage relative to the side length of the blue square?
Sources:Topics:Geometry -> Plane Geometry Geometry -> Area Calculation Algebra -> Word Problems Arithmetic -> Percentages -
THE TWO AEROPLANES
A man recently bought two aeroplanes, but afterwards found that they would not answer the purpose for which he wanted them. So he sold them for £`600` each, making a loss of `20` per cent, on one machine and a profit of `20` per cent, on the other. Did he make a profit on the whole transaction, or a loss? And how much? Sources: -
THE JUNIOR CLERK'S PUZZLE
Two youths, bearing the pleasant names of Moggs and Snoggs, were employed as junior clerks by a merchant in Mincing Lane. They were both engaged at the same salary—that is, commencing at the rate of £`50` a year, payable half-yearly. Moggs had a yearly rise of £`10`, and Snoggs was offered the same, only he asked, for reasons that do not concern our puzzle, that he might take his rise at £`2, 10`s. half-yearly, to which his employer (not, perhaps, unnaturally!) had no objection.
Now we come to the real point of the puzzle. Moggs put regularly into the Post Office Savings Bank a certain proportion of his salary, while Snoggs saved twice as great a proportion of his, and at the end of five years they had together saved £`268, 15`s. How much had each saved? The question of interest can be ignored.
Sources:- Amusements in Mathematics, Henry Ernest Dudeney Question 26