# What percentage is 41 kg of 287 kg

## Calculating percentages of the solutions to the tasks

#### 1. There are 17 boys and 8 girls in one class.

What percentage of boys or girls are in the class?

17 \, boys + 8 \, girls = 25 \, pupils \, \ widehat {=} \, 100 \%

We are looking for \, the \, percentage: p \% = \ frac {W} {G}

\ underline {Boys:} \ newline G = 25 \ newline W = 17 \ newline p \% = \ frac {17} {25} = \ underline {\ underline {68 \%}} | \ underline {Girls:} \ newline G = 25 \ newline W = 8 \ newline p \% = \ frac {8} {25} = \ underline {\ underline {32 \%}} |

The proportion of boys is 68% and that of girls 32%.

#### 2. The list price of a car is € 23,925. The customer gets the car for 21054 €.

What percentage is this price below the list price?

List price: 23925 \, €

Purchase price: 21054 \, €

We are looking for \, the \, percentage: p \% = \ frac {W} {G}

G = 23925 € \ newline W = 23925 € - 21054 € = 2871 €

p \% = \ frac {2871 €} {23925 €} = \ underline {\ underline {12 \%}}

The purchase price is 12% below the list price.

#### 3. The price of buying a car is € 1920.45, since the payment is made in installments.

What was the original price of the car if the price increase was 10.5%?

10.5 \% \, of the \, basic value \, is 1920.45 \, €

We are looking for \, the \, basic value: G = \ frac {W} {p \%}

Percentage \, p \% = 10.5 \% \ newline Percentage \ newline W = € 1920.45

G = \ frac {1920.45 €} {10.5 \%} = \ underline {\ underline {18290 \, €}}

The original price of the car was € 18,290.

#### 4. A car uses 47 liters of petrol over 400 km, another car uses 65.8 liters over 700 km. What percentage is the consumption of one of the two cars lower than that of the other?

What percentage is the consumption of one of the two cars lower than that of the other?

Consumption \, on \, 100km:

Auto \, I: \ frac {47} {4} = 11.75 \ frac {liter} {100km} \ newline Auto II: \ frac {65.8} {7} = 9.4 \ frac {liter} { 100 km}

Auto \, I \, has \, the \, highest \, consumption \ Rightarrow G = 11.75 \, \, \, W = 11.75-9.4 = 2.35

Wanted \ is \, the \, percentage: p \% = \ frac {W} {G} = \ frac {2,35} {11,75} = \ underline {\ underline {20 \%}}

The consumption of Auto II is 20% less than that of Auto I.

#### 5. The price of a car increases by paying in installments from € 38950 to € 42650.

What percentage is the surcharge?

G = 38950 € \ newline W = 42650 € - 38950 € = 3700 €

Wanted \, is \, the \, percentage: p \% = \ frac {W} {G} = \ frac {3700 €} {38950 €} \ approx \ underline {\ underline {9.5 \%}}

The surcharge for partial payments is around 9.5%.

#### 6. In a department store, after a price increase of 5%, four winter tires are offered together for € 327.60.

How expensive were the tires before?

Increased \, basic value

The \, new \, price \, is \ 105 \% \, of the \, basic value.

\ Rightarrow 105 \% \ cdot G = 327.60 \, € \ Leftrightarrow G = \ frac {327.60 €} {105 \%} = 327.60 €: \ frac {105} {100} = 327.60 € \ cdot \ frac {100} {105} = \ underline {\ underline {312 €}}

Before the price increase, the tires cost € 312.

#### 7. A legal assistant pays 22% wage tax per month, that is € 435.60. What is your gross wage?

Percentage \, p \% = 22 \% \ newline Percentage \ newline W = 435.60 \%

We are looking for \, the \, basic value:

G = \ frac {W} {p \%} = \ frac {435.60 €} {22 \%} = 435.60 €: \ frac {22} {100} = 435.60 € \ cdot \ frac { 100} {22} = \ underline {\ underline {1980 €}}

The gross salary of the legal assistant is 1980 €.

#### 8. A bricklayer receives an hourly wage of € 11.76 because he works in piecework.

How many percent is it above the normal wage of € 11.20?

Base value \, G = 11.20 € \ newline percentage value \, W = 11.76 € - 11.20 € = 0.56 €

We are looking for \, the \, percentage \, p \% = \ frac {W} {G} = \ frac {0.56 \, €} {11.20 \, €} = \ underline {\ underline { 5 \%}}

The piecework wage is 5% above the normal wage.

#### 9. After deducting 32.8% taxes, a saleswoman receives a net salary of € 1,428.

What is the gross salary?

Percentage \, p \% = 32.8 \%

We are looking for \, the \, reduced \, basic value

The \, net salary \, is 67.2 \% of the \, base value

\ Rightarrow 0.672 \ cdot G = 1428 € \ Leftrightarrow G = \ frac {1428 €} {0.672} = \ underline {\ underline {2125 €}}

The gross salary of the specialist saleswoman is 2125 €.

#### 10. The hourly wage of an industrial mechanic of € 11.20 is to be increased by 2.5%.

What is the new hourly wage?

Base value \, G = 11.20 \, € \ newline percentage \, p = 2.5 \%

Wanted \, is \, the \, percentage value:

W = G \ cdot p \% = 11.20 € \ cdot \ frac {2.5} {100} = 0.29 € (wage increase)

New \, wage: 11.20 € + 0.28 € = \ underline {\ underline {11.48 €}}

The industrial mechanic's new hourly wage is € 11.48.

#### 11. An architect charges a builder 8.5% of the building costs as a fee.

How high is his fee for a single-family home with construction costs of € 290,300?

Percentage \, p \% = 8.5 \% \ newline basic value \, G = 290300 \, €

We are looking for \, the \, percentage value:

W = G \ cdot p \% = 290300 \ cdot \ frac {8.5} {100} = \ underline {\ underline {24675.50 €}}

The architect's fee is € 24,675.50.

#### 12. A terraced house should be built for 244750 €. The costs rose to € 259 435 during the construction period.

What% was the price increase?

Base value \, G = 244750 \, € \ newline percentage value \, p \% = 259435 € - 244750 € = 14685 €

We are looking for \, the \, percentage \, p \% = \ frac {W} {G} = \ frac {14685 €} {244750 €} = \ underline {\ underline {6 \%}}

The price increase was 6%.

#### 13. A construction pit with a fixed soil volume of 400 m^{3} should be excavated.

How many trucks with 12 m^{3} Cargo is required for removal if the soil is loosened by 14%?

Basic value \, G = 400m³ \ newline percentage \, p \% = 14 \%

We are looking for \, the \, percentage value:

W = G \ cdot p \% = 400m³ \ cdot \ frac {14 \%} {100} + 56m³ = 456m³

To be removed \, 400m³ + 56m³ = 456m³ are

A \, truck \, holds \, 12m³ \, earth \ Leftrightarrow number of trucks = \ frac {456m³} {12 \ frac {m³} {trucks}} = \ underline {\ underline {38 \, trucks}}

38 trucks are required to transport the earth away.

#### 14. A hardware store gives members of settler communities a 6% discount on all purchases. How much would a member have to pay for a lawnmower that normally costs € 164.50.

Base value \, G = 164.50 \, € \ newline percentage \, p = 6 \%

We are looking for \, the \, percentage value:

W = G \ cdot p \% = 164.50 € \ cdot \ frac {6} {100} = 9.87 € \ (discount)

Final price = € 164.50 - € 9.87 = \ underline {\ underline {154.63 \, €}}

A member of the settler community has to pay € 154.63 for the lawn mower.

#### 15. A customer buys an exercise bike in a sports shop for € 399.50. As a member of a sports club, she receives a discount and pays only € 367.54.

What% was the discount?

Base value \, G = 399.50 € \ newline percentage value \, W = 399.50 € - 367.54 € = 31.96 €

We are looking for \, the \, percentage \, p \% = \ frac {W} {G} = \ frac {€ 31.96} {€ 399.50} = \ underline {\ underline {8 \%} }

The price reduction was 8%.

#### 16. A gardener buys a lawn tractor and receives a discount.

What percentage of discount does he get if he only pays 1261.95 € instead of € 1342.50?

Base value \, G = 1342.50 € \ newline percentage value \, W = 1342.50 € - 1261.95 € = 80.55 €

We are looking for \, the \, percentage \, p \% = \ frac {W} {G} = \ frac {80.55 \, €} {1342.50 \, €} = \ underline {\ underline { 6 \%}}

The gardener receives a 6% discount.

#### 17. A hobby gardener pays € 184.30 for a chainsaw after deducting a 3% discount.

What was the original selling price?

Decreased \, basic value

The \, new \, price \, is \, 97 \% \, of the \, basic value

\ Rightarrow 0.97 \ cdot G = 184.30 € \ Leftrightarrow G = \ frac {184.30 €} {0.97} = \ underline {\ underline {190 €}}

The original price of the chainsaw was € 190.

#### 18. The basic price of a car is € 27,500. The special equipment increases the price by 1000 €. For cash payments, the buyer receives a 12% discount.

What percentage of the basic price has actually been paid?

Base price: € 27,500

Special equipment: 1000 €

Discount: W = G \ cdot p \% = 28500 € \ cdot \ frac {12} {100} = 3420 €

Percentage: p \% = \ frac {W} {G}

Basic price \, and \, special equipment: € 27,500 + € 1,000 = € 28,500

Less \, 12 \% \, discount: 28500 \, € - 3420 \, € = \ underline {\ underline {25080}} \, €

With \, W = 27500 € - 25080 € = 2420 €

\ Rightarrow p \% = \ frac {2420 €} {27500 €} = 8.8 \%

Actually \ to \, pay: 100 \% - 8.8 \% = \ underline {\ underline {91.2 \%}}

In fact, 91.2% of the base price was paid.

### Here you will find the tasks calculating percentages I.

**The theory for this can be found under ****Introduction to the percentage calculation.**

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