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Solved problems for the chapter:

Percentage changes

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Proportion and percentage change

1. Proportion

1.1. Direct proportion

1.2. Inverse proportion

2. Change

2.1. Relative change

2.2. Percentage Change

2.2.1. Relationship between relative change and percentage change

3. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:percentage_changes/5232/

Example 1.

The original price of a roller skate is € 150. First, the price was reduced by 33%, and then by another 20% from the already reduced price. How much does the roller skate cost after the second reduction?

Example 2.

A bouquet of 20 tulips cost € 30. After a price reduction, a bouquet of 35 tulips now costs € 31.5. By what percentage has 1 tulip reduced in price?

A hairdresser charges € 40 per hour. Then she made her services more expensive. Now € 40 counts for 40 minutes. What is the percentage increase in the price?

700 olive trees were planted on a plantation. In the first year, 20% of the olive trees was removed due to drought. The following year, three-quarters of the olives yielded three-quarters of trees. How many olive trees was produced in the second year?

10 pieces of cake sometimes cost £25. They then lowered the price of their products at the confectionery. 8 pieces of cake now cost £16. By what percentage was the price reduced?

If a kitchen cost pounds in January. The cost was first raised in April by and then in May by .

What was the price of the kitchen after the last price increase?
What is the percentage increment?

The price per square meter of forest is pounds. It is then increased in March by and then in June by . With the use of a calculator, calculate the price per square meter of forest after the June increase?

A factory made products in 2012, and in 2013 it made more products. What is the percentage increment in 2013?

A journalist wrote in the newspaper that the price of a barrel of petrol has dropped by as much as 100% this year. Calculate how much a barrel of petrol costs after the reduction, if it cost pounds before the reduction and comment on the journalist's statement.

10.

In January, a dress cost pounds. In February, it increases by , and in March, it decreases by . What is the price of the dress after both changes?

11.

The price of the product was N pounds. It was first increased by and then reduced by twice in a row. By what percentage is the final price of the product lower than its initial price?

12.

A factory in 2011 produced products, the following year the factory increased its production by , and in 2013 it was decreased by due to low demand. How many products did the factory produce in 2013?

13.

There are members in a sport club initially. The number of members was increased by as much as in a year and was later decreased by members the following year. How many members does the sport club have now?

14.

If a washing machine cost pounds. In August it went up by , in September by , and in October it went up by . What is the price of the washing machine after the last price change in October?

15.

If and . Increase the number by and decrease the number by . Calculate the sum of the two new numbers .

16.

The price of a coat has risen by , so it now costs pounds. What was the initial cost of the cost before the price increased?

17.

Write the price increase of a product as a percentage if:

The product is more expensive by a fifth of the original price.
The product costs six times the original price.

18.

Cenet and Ana received the same monthly scholarship of pounds from the beginning of their studies. The amount of their scholarship increases every 12 months, Cenet’s by while Ana’s by pounds.

How much monthly scholarships will Cenet have after months?
Which of them will have a higher monthly scholarship after months and by what percentage?
Calculate the sum of all scholarships that Cenet will receive in years.

19.

September 2000, we paid tolars for a liter of heating oil, and May 2004, we paid tolars.

By how many percent was the price of heating oil in May 2004 lower than the price in September 2000?
How much tolars will we pay in September 2000 for a full fuel oil in a cube tank with dimensions of m, m and m? Draw a sketch of the tank.
Is liters of heating oil sufficient for heating from October 1 to March 15 of the following year, if the daily consumption is litres?