Percentages

Theory

Problems

1. The student read 138 pages, which is 23% of all pages in the book. How many pages are in the book?

2. Arrange 80 notebooks into two piles so that the number of notebooks in one of them is 60% of the number of notebooks in the other stack.

3. When 12.5% of the milk in the first can was poured from the first can into the second, the milk in the cans became equal, 35 litres each. How much milk was in the second can?

4. The multiplicand was increased by 50%, and the multiplier was decreased by 50%. How has the work changed?

5. Which is greater: 15.43% of 5 or 5% of 15.43?

6. How will the price of a product change if it is first increased by 100% and then decreased by 50%?

7. The price of potatoes was increased by 20%. After some time, the price was reduced by 20%. When were potatoes cheaper: before the increase or after the decrease?

8.

a) A, B and C competed in a 100 m race. When A finished, B was 10 m behind him. When B finished, C was 10 m behind. How much was C behind A when A finished the race?
b) In one store, prices were reduced by 10%, and then by another 10% (from the new level). And in another, prices were simply immediately reduced by 20%. What is more profitable for the buyer?

9. Over the spring, Smith lost 25% in weight, over the summer he gained 20%, over the fall he lost 10%, and over the winter he gained 20%. Has he lost weight or gained weight over the year?

10. Pacific Ocean water contains 3.5% salt (by weight). How much fresh water must be added to 40 kg of such water so that the salt content in the mixture is 0.5%?

11. From 22 kilograms of fresh mushrooms, 2.5 kilograms of dried mushrooms containing 12% water are obtained. What is the percentage of water in fresh mushrooms?

12.
a) What is the smallest number of participants in a levitation club if there are less than 50% of boys in it, but more than 40% of them?
b) For what smallest natural number n is there a fraction with denominator n located between the numbers 0.4 and 0.5?

13. The number 51.2 was increased three times by the same percentage, and then decreased three times by the same percentage. The result was 21.6. By how many percentages was this number increased and then decreased?

14. The company was given the task of reducing the volume of manufactured products by 51% in two years. Every year they demand a reduction by the same percentage. By how much?

15. There were V litres of alcohol in a vessel. Some fraction of it was poured out and the same amount of water was added. Then, after mixing, the same fraction was poured out and the vessel was again filled with water. There was three times less alcohol in the vessel than water. What part was poured out?

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