Deck 3: Ratios and Proportions

Question 1

A punch recipe calls for orange juice, ginger ale, and vodka to be mixed in the ratio of 4.5:2.5:1. How much orange juice and vodka should be mixed with 2-litre bottle of ginger ale?

A) 3.6 litres orange juice; 0.8 litres vodka
B) 3.5 litres orange juice; 0.75 litres vodka
C) 6 litres orange juice; 0.1.25 litres vodka
D) 5 litres orange juice; 1.1 litres vodka
E) 4.1 litres orange juice; 0.9 litres vodka

Answer 1

3.6 litres orange juice; 0.8 litres vodka

Question 2

Aaron, Luc and Isaac invested in a business in the ratio of 3.5: 5: 7.5. The factory that they leased requires renovations of $125,000. If the partners want to maintain their investments in the business in the same ratio, how much should each partner pay for the renovations?

A) $58,593.75; $27,343.75; $39,062.50
B) $35,000; $50,000; $75,000
C) $20,000; $40,000; $60,000
D) $27,343.75; $58,593.75; $39,062.50
E) $27,343.75; $39,062.50; $58,593.75

Answer 2

$27,343.75; $39,062.50; $58,593.75

Question 3

Mr. Malik is considering a larger house in the same area. Currently the taxes on his $250,000 home are $3,000 per year. If he expects that the taxes on other homes in the area are in the same ratio as the assessed values, what amount of taxes can Mr. Malki expect to pay on a house assessed at $300,000?

A) $3,200
B) $3,600
C) $3,500
D) $3,000
E) $4,000

Answer 3

$3,600

Question 4

The current exchange rates show that C$1.00 = US$0.9672. If you have $120 Canadian dollars, what is the equivalent amount in US dollars?

A) US$116.06
B) US$143.71
C) US$124.07
D) US$83.50
E) US$100

Question 5

Express the ratio 0.25: 1.40: 8.50 in its lowest terms:

A) 1: 5.6: 34
B) 5: 14: 85
C) 5: 28: 170
D) 2: 28: 170
E) 2: 14: 85

Question 6

Solve the proportion: 0.75 : 5.5 = 6 : x

A) 40
B) 44
C) 8
D) 6
E) 24

Question 7

Based on past experience, a production process requires 15 hours of direct labour and 2 assemblers for every $450 of raw materials. If the company has budgeted for $33,750 worth of raw materials, how many hours of direct labour and how many assemblers will the company require?

A) 112.5; 15
B) 2,250; 300
C) 1,125; 150
D) 112.5; 150
E) 1,125; 300

Question 8

Nitin and Sam have invested in a partnership in the ratio of 3:5. If Sam adds another $10,000 to the business, how much should Nitin invest in order to maintain the same ratio?

A) $10,000
B) $3,000
C) $5,000
D) $6,000
E) $12,000

Question 9

Kuldip and Jane invested $35,000 and $55,000 respectively in a partnership. Kuldip added another $20,000 and Jane wants to add enough to maintain their investments in the original ratio. How much should Jane invest in order to maintain the same ratio?

A) $12,727
B) $30,000
C) $35,000
D) $31,429
E) $25,000

Question 10

Jane, Lynda, and Ginny run a consignment dress store. The partnership agreement states that the profits are distributed according to the hours each works in the store. For the month of July, profits are $8,500. The hours worked by Jane, Lynda and Ginny are 170, 190, and 200 respectively. How should the month's profits be allocated?

A) $2,000; $3,000; $3,000
B) $3,000; $3,000; 2,000
C) $2,883.93; $2,580.36; $3,035.71
D) $3,035.71; $2,883.93; 2,580.36
E) $2,580.36; $2,883.93; $3,035.71

Question 11

Sam, Domenic, and Sal invested $200,000, $125,000 and $150,000 respectively in a business. In order to expand a further investment was required. Sal invested $200,000. If the other partners agreed to provide capital in the same ratio as the initial investment, how much did Sam and Domenic invest?

A) $166,667; $266,667
B) $250,000; $175,000
C) $266,667; $166,667
D) $175,000; $250,000
E) $266,667; $250,000

Question 12

Solve the proportion: 2.6 : 5.5 : 10 = 13 : x : y

A) 50; 27.5
B) 5.5; 20
C) 27.5; 50
D) 11; 20
E) 26; 11

Question 13

A college allows parking permits for students in the ratio of 5.5 students to a parking permit. The college currently has 11,000 students. The student council did a survey and found that the ratio should be 4:1. The college has agreed to add the extra parking spaces. How many more spaces are required to meet the 4:1 ratio?

A) 2,750
B) 2,200
C) 1,250
D) 1,150
E) 750

Question 14

Solve the proportion: 4 : 7 : 8 = 6 : x : y

A) 12; 10.5
B) 10.5; 12
C) 6; 8
D) 8; 10.5
E) 8; 12

Question 15

Solve the proportion: 2 : 5 = 6 : y

A) 15
B) 5
C) 10
D) 6
E) 12

Question 16

During 2016, Acme Company's total overhead of $685,000 was allocated as follows: 18% to division A, 42% to division B, and the remainder to division C. What is the ratio of the overhead in division A to the overhead in division B to the overhead in division C in the lowest terms?

A) 18: 42: 40
B) 9: 21: 20
C)
D) 10: 23: 22

Question 17

A gym club membership costs $499 for two years. A member may cancel at any time and a refund less a $75 administration fee will be issued. The notice of cancellation must be received by the 15^th of the month in order for the cancellation to be effective for the following month. Najib purchased a membership on March 1^st last year, and decided to cancel it on June 10^th of this year. How much of a refund will Najib receive?

A) $166.33
B) $332.67
C) $257.55
D) $91.33
E) $112.13

Question 18

Sam, Domenic, and Sal invested $100,000, $125,000 and $150,000 respectively in a business. In order to expand a further investment was required. Sal invested $200,000. If the other partners agreed to provide capital in the same ratio as the initial investment, how much did Sam and Domenic invest?

A) $166,667; $133,333
B) $133,333; $166,667
C) $150,000; $175,000
D) $175,000; $150,000
E) $133,333; $150,000

Question 19

Sam, Domenic, and Sal invested $100,000, $150,000 and $75,000 respectively in a business. The profits from last year were $80,000. How much of the profits should each partner receive?

A) $24,615.38; $36,923.08; $18,461.54
B) $25,000; $35,000; $10,000
C) $20,000; $35,000; $15,000
D) $24,615.38; $18,461.54; $36,923.08
E) $36,923.08; $18,461.54; $24,615.38

Question 20

Susan, Lynda, and Monica opened a consignment dress shop. The partnership agreement states that the responsibilities for the provision of capital are in the ratio of 2.5: 3.75: 4.5. If the total investment in the business was $365,500, how much did each partner invest?

A) $153,000; $85,000; $127,500
B) $175,000; $150,000; $40,500
C) $150,000; $175,000; $40,500
D) $85,000; $127,500; $153,000
E) $210,000; $115,000; $35,500

Question 21

The current exchange rates show that US$1.00 = €0.7700. If you have $450 US dollars to exchange and the currency exchange charges 2.5% on all transactions, how many euros will you be able to buy?

A) €346.50
B) €337.84
C) €584.42
D) €569.81
E) €450

Question 22

You can buy euros at a currency exchange store or at the airport. If you want to buy €250, would it be better to pay a 1% transaction fee or a flat service charge of $10.00? Use C$1.00 = €0.7448 as the exchange rate.

A) 1% transaction fee is more expensive by $6.64
B) 1% transaction fee is less expensive by $6.64
C) flat service charge is less expensive by $6.64
D) flat service charge is more expensive by $6.64
E) no difference in fee

Question 23

The current exchange rates show that US$1.00 = €0.7700. If you have $600 US dollars, what is the equivalent amount in euros?

A) €462.00
B) €803.40
C) €779.22
D) €750
E) €450

Question 24

How much will it cost in C$ to buy €2,000 in traveller's cheques if the exchange rate is C$1.00 = €0.7448, and the financial institution charges a fee of ½%?

A) $2,698.71
B) $3,207.17
C) $2,685.28
D) $1,247.20
E) $1,497.05

Question 25

If the C$ strengthens by 2% relative to the US$ (US$1.00 = C$1.0339), what will be the new value for the US$ per C$1.00?

A) US$0.8350 per C$1.00
B) US$1.0339 per C$1.00
C) US$0.8034 per C$1.00
D) US$0.96721 per C$1.00
E) US$0.9866 per C$1.00

Question 26

If the C$ weakens by 1½% relative to the US$ (US$1.00 = C$1.0339), what will be the new value for the US$ per C$1.00?

A) US$0.95270 per C$1.00
B) US$0.96721 per C$1.00
C) US$0.8564 per C$1.00
D) US$1.0339 per C$1.00
E) US$0.8572 per C$1.00

Question 27

The current exchange rates show that C$1.00 = €0.7448. If you have $200 Canadian dollars, what is the equivalent amount in euros?

A) €320.71
B) €148.96
C) €136.50
D) €268.53
E) €150.70

Question 28

The current exchange rates show that C$1.00 = £0.6370. If you have C$250, what is the equivalent amount in British pounds?

A) £392.46
B) £105
C) £159.25
D) £430.97
E) £200

Question 29

The current exchange rates show that C$1.00 = €0.7448. If you have $1,000 Canadian dollars to exchange and the currency exchange charges 4% on all transactions, how many euros will you be able to buy?

A) €1,342.64
B) €1063.59
C) €1,288.94
D) €715.008
E) €960

Question 30

If the C$ weakens by 1% relative to the euro (C$1.00 = €0.7448), what will be the new value for the euro per C$1.00?

A) 0.6298 per C$1.00
B) 0.6236 per C$1.00
C) 0.7374 per C$1.00
D) 0.6174 per C$1.00
E) 0.6860 per C$1.00

Question 31

If the C$ weakens by 2½% relative to the euro (C$1.00 = €0.7448), what will be the new value for the euro per C$1.00?

A) €0.6298 per C$1.00
B) €0.6236 per C$1.00
C) €0.6299 per C$1.00
D) €0.7262 per C$1.00
E) €0.6860 per C$1.00

Question 32

A litre of gas costs €1.00 in France. What would be the equivalent cost in Canada? Use C$1.00 = €0.7448 as the exchange rate.

A) $0.62
B) $0.74
C) $0.85
D) $1.40
E) $1.34

Question 33

A bag of popcorn costs C$1.99 in Canada, and the same bag of popcorn costs US$1.99 in Morgan Hill, California, USA. What percentage more is the cost of the bag of popcorn in the US than in Canada? Use US$1.00 = C$1.0339 as the exchange rate.

A) 16.5%
B) 80.24%
C) 3.39%
D) 83.5%
E) 19.67%

Question 34

If the C$ strengthens by 3% relative to the euro (C$1.00 = €0.7448), what will be the new value for the euro per C$1.00?

A) €0.7671 per C$1.00
B) €0.7049 per C$1.00
C) €0.7429 per C$1.00
D) €0.4797 per C$1.00
E) €0.8107 per C$1.00

Question 35

If the C$ weakens by 2½% relative to the US$ (US$1.00 = C$1.0339), what will be the new value for the US$ per C$1.00?

A) US$0.8146 per C$1.00
B) US$0.9430 per C$1.00
C) US$0.8665 per C$1.00
D) US$1.0339 per C$1.00
E) US$0.8651 per C$1.00

Question 36

The current exchange rates show that US$1.00 = C$1.0339. If you have $375 US dollars, what is the equivalent amount in Canadian dollars?

A) C$313.13
B) C$362.70
C) C$300
D) C$315.76
E) C$387.71

Question 37

The current exchange rates show that C$1.00 = US$0.9672. If you have $500 Canadian dollars to exchange and the currency exchange store charges 2% on all transactions, how many US dollars will you be able to buy?

A) US$506.62
B) US$425.85
C) US$473.93
D) US$483.60
E) US$586.82

Question 38

If the C$ strengthens by 1% relative to the US$ (US$1.00 = C$1.0339), what will be the new value for the US$ per C$1.00?

A) US$0.8350 per C$1.00
B) US$0.8434 per C$1.00
C) US$1.0339 per C$1.00
D) US$0.9769 per C$1.00
E) US$0.9672 per C$1.00

Question 39

If the C$ strengthens by 4% relative to the euro (C$1.00 = €0.7448), what will be the new value for the euro per C$1.00?

A) €0.5987 per C$1.00
B) €0.7485 per C$1.00
C) €0.4454 per C$1.00
D) €0.7496 per C$1.00
E) €0.7746 per C$1.00

Question 40

A hamburger in Canada costs C$5.00, and the same hamburger costs €5.00 in France. What percentage more is the cost of a hamburger in France? Use C$1.00 = €0.7448 as the exchange rate.

A) 37.6%
B) 39.6%
C) 62.4%
D) 34.3%
E) 0%

Question 41

Carol bought 25.5 hectares of land for $63,000. If she buys another 80 hectares of land at the same price per hectare as her first purchase, how much must she pay for her second purchase?

A) $247,058.82
B) $197,647.06
C) $200,812.50
D) $260,647.06
E) $308,823.53

Question 42

If the "basket" of goods and services included in the consumer price index (CPI) cost $21,350 in the base year (when the CPI = 100) and currently costs $28,550, what is the current CPI?

A) 133.72
B) 128.63
C) 74.78
D) 125.08
E) 139.77

Question 43

The CPI increased from 125.0 to 132.0 over a three-year period. If a person earned $40,000 at the beginning of the three-year period, how much would they have to earn at the end of the three-year period to maintain the same purchasing power?

A) $42,800
B) $42,240
C) $40,933
D) $42,121
E) $40,250

Question 44

Sally earns $25 per hour today. Seven years ago she earned $20.75 per hour. During the seven-year period the CPI rose from 136.5 to 158.2. Has Sally's buying power increased or decreased and by how much in current year's dollars?

A) increased by $3.61
B) decreased by $3.61
C) decreased by $0.95
D) increased by $0.95
E) increased by $1.40

Question 45

The price of a box of chalk has increased from $.89 to $1.39 over a ten-year period. What index number would represent the change in price over the ten-year period?

A) 150.0
B) 156.2
C) 136.0
D) 142.0
E) 148.2

Question 46

Total overhead of $235,000 is allocated according to the proportion of labour hours. Department A used 1830 hours, department B used 1635 hours, and department C used 1760 hours. What amount of overhead should be allocated to department C?

A) $119,365.08
B) $155,842.11
C) $115,634.92
D) $82,306.22
E) $79,157.89

Question 47

The price of a laser printer dropped from $299.99 to $175. What index number would represent the change in price?

A) 125.0
B) 75.0
C) 58.3
D) 71.4
E) 41.7

Question 48

The basket of goods and services included in the Consumer Price Index cost $425 in the base year. If the same basket cost $575 ten years later, what was the CPI on that date?

A) 73.9
B) 126.1
C) 115.0
D) 130.4
E) 135.3

Question 49

Express the following ratio whose smallest term is 1. 3: 21: 0.75

A) 1: 7: 0.25
B) 3: 21: 1
C) 11: 13: 1
D) 1: 7: 25
E) 4: 28: 1

Question 50

Victoria is going to ask for a raise. Over the past year, the CPI has gone from 119.6 to 122.6. Victoria now earns $45,000. What is the minimum raise that Victoria should ask for in order to maintain the same buying power?

A) $46,129
B) $46,350
C) $46,101
D) $46.500
E) $46,100

Question 51

If the US$ strengthens by 2% relative to the euro (US$1.00 = €0.746826), what will be the new value for the euro per US$1.00?

A) €0.7618 per US$1.00
B) €0.7322 per US$1.00
C) €0.7319 per US$1.00
D) €0.7621 per US$1.00
E) €0.8962 per US$1.00

Question 52

Sam is going to ask for a raise. Over the past year, the CPI has gone from 129.9 to 131.9. Sam currently earns $42,500. What is the minimum raise that Sam should ask for in order to maintain the same buying power?

A) $43,350
B) $43,144
C) $44,000
D) $43,500
E) $43,154

Question 53

If the US$ weakens by 5% relative to the euro (US$1.00 = €0.746826), what will be the new value for the euro per US$1.00?

A) €0.7842 per US$1.00
B) €0.7095 per US$1.00
C) €0.7861 per US$1.00
D) €0.7113 per US$1.00
E) €0.7855 per US$1.00

Question 54

Express the following ratio in its lowest terms. 76: 44: 8

A) 38: 22: 1
B) 38: 11: 2
C) 9: 5: 1
D) 19: 11: 2
E) 6: 3: 1

Question 55

Nitin earns $15 per hour today. Five years ago he earned $11.75 per hour. During the five-year period the CPI rose from 136.5 to 147.6. Has Nitin's buying power increased or decreased and by how much in current year's dollars?

A) increased by $2.37
B) decreased by $2.37
C) increased by $2.29
D) decreased by $2.29
E) increased by $1.95

Question 56

Suppose C$1.00 is equivalent to US$0.9672. What $C amount would it cost to purchase US$1565? (Ignore any commission.)

A) $1,513.67
B) $1932.31
C) $2114.28
D) $1,618.07
E) $2762.95

Question 57

The CPI increased from 130.0 to 135.0 over a two-year period. If a person earned $35,000 at the beginning of the two-year period, how much would they have to earn at the end of the two-year period to maintain the same purchasing power?

A) $36,346
B) $36,750
C) $36,296
D) $36,500
E) $40,125

Question 58

Express the following ratio in its lowest terms. 130: 290: 60

A) 2: 4: 1
B) 26: 58: 12
C) 65: 145: 30
D) 58: 26: 12
E) 13: 29: 6

Question 59

Three partners share the partnership's profit according to the proportion of the business each owns. Ms. A owns 30%, Mr. B owns 25% and Ms. C owns the remainder. What profit would Mr. B receive if Ms. A receives $32,500?

A) $108,333.33
B) $8,125.00
C) $24,375.00
D) $27,083.33
E) $30,875.00

Question 60

The basket of goods and services included in the Consumer Price Index cost $35,750 in the base year. If the same basket cost $43,000 six years later, what was the CPI on that date?

A) 83.1
B) 116.7
C) 72.5
D) 120.3
E) 118.4

Question 61

Analysis of Suzanne's sales, showed 12% in the West Region, 36% in the North Region, 6% in the South Region and the 46% in the East Region. The ratio of sales expressed in its smallest term is 2:6:1:2.67

Question 62

Solve for X in the proportion: 3: 5 = X: 20

A) 15
B) 12
C) 3
D) 0.75
E) 26.666

Question 63

On a typical day Generous Motors sells 3,600 vans, 1,500 pickup trucks, and 7,800 passenger cars. What is the sales ratio of cars to vans to pickups?

A) 36: 15: 78
B) 1,560: 720: 300
C) 26: 12: 5
D) 78: 15: 36
E) 12: 5: 26

Question 64

Mary paid $1,500 for car insurance at the beginning of the year. After 5 months she cancelled the insurance and was given a pro-rated refund based on the number of months remaining on the policy less a service charge of $100. How much money did she get back?

A) $500
B) $600
C) $625
D) $775
E) $875

Question 65

Mike, Don, and Matt entered a partnership agreement by contributing $17,000, $42,500 and $54,400 respectively. The proportion of Mike to Don to Matt's partnership interests is 1:2.5:3.2.

Question 66

A car requires 8 litres of gasoline to go 88 km. How many litres of gasoline will be required to go 16 km at the same rate of consumption?

A) 1.6
B) 0.5
C)
D) 176
E) 5.5

Question 67

Betty and Lois have already invested $12,450 and $16,600 respectively. If Betty invests another $6,000 what amount should Lois contribute to maintain their investments in the same ratio?

A) $6,000
B) $7,000
C) $8,000
D) $9,000
E) $4,000

Question 68

Solve for t in 1.65: 5 = 0.75: t

A)
B) 0.44
C) 1.2375
D) 0.2475
E)

Question 69

The Alberta government's budget is estimated to be $1.84 billion for healthcare, $2.3 billion for education and $.46 billion on social services. Expressed as a proportion the ratio is 0.4:0.5:0.1.

Question 70

Ajax Corporation has $10 million in debt and $75 in equity. The debt to equity ratio in lowest terms is 2:15.

Question 71

Axel, Bonita, and Chip are partners in business. The ratio of ownership of the partnership between Axel, Bonita, and Chip respectively is 5:4:10. If Bonita's share is worth $28,000 what is the value of the whole business?

A) $56,000
B) $35,000
C) $112,000
D) $133,000
E) $70,000

Question 72

To raise money for her hockey team, Juliana collected a total of $264. Her uncle Vic donated $96, her uncle Dave donated $48 and her aunt Karen donated the rest. In lowest terms, express the ratio of the donations of Vic, Dave and Karen.

A) 4: 2: 5
B) 5: 12: 26
C) 2: 5: 4
D) 4: 2: 11
E) 5: 2: 4

Question 73

Last year, a company's salespersons, A, B, and C recorded sales as follows: "A" recorded three sevenths (3/7) of the total, "B" recorded one quarter (1/4) of the total and "C" recorded the rest of the sales. Express, in lowest terms, the sales ratio of A: B:C.

A) 3: 7: 4
B) 7: 4: 1
C) 3: 1: 6
D) 21: 7: 28
E) 12: 7: 9

Question 74

Hockey goals and assists each count as one point. Anthony's ratio of goals to assists is 2:5. Last season he collected a total of 91 points. How many goals did Anthony score?

A) 65
B) 35
C) 26
D) 78
E) 13

Question 75

Bonus money totalling $920,000 is to be shared by Dave, Claude, Marcel, and Larry by the ratio 15: 11: 8: 6. How much will Dave receive?

A) $253,000
B) $460,000
C) $345,000
D) $368,000
E) $312,000

Question 76

Last year the team won 34 games and lost 17. This year they will play a total of 15 more games than they played last year. How many games will they have to win this year to maintain the ratio of wins to losses from last year? (There are no tie games.)

A) 51
B) 24
C) 10
D) 44
E) 48

Question 77

Solve for X in the proportion: 4.75: 60 = 190: X

A) 24
B) 1504
C) 2,400
D) 76
E) 1800

Question 78

Rodger, Dodger, and Codger own a business in the ratio of 12: 7: 9. The value of the business is $560,000. If Codger sells his share to Dodger, what will be the new ownership ratio in the form Rodger: Dodger?

A) 4: 3
B) 21: 7
C) 3: 1
D) 4: 5
E) 3: 4

Question 79

A lottery prize was shared by Andy, Betty, and Chris by the ratio of 15:12:27. If Andy received $ 4,500, how much did Chris get?

A) $11,700
B) $8,100
C) $3,600
D) $16,200
E) $9,900

Question 80

Express the following ratio as an equivalent ratio whose smallest term is 1. 0.75: 3

A) 0.25: 1
B) 4: 1
C) 3: 12
D) 2.25: 1
E) 1: 4