### Ratio And Proportion

Worked Exercise

- Muraya and Dan each made 126kg of a mixture of maize and beans. Muraya mixed maize and beans in the ratio 4:3 while Dan mixed maize and beans in the ratio 4:3 while Dan mixed maize and beans in the ratio of 5:4. How many more kilograms?
- 2
- 3
- 4
- 6

Working

In Muraya’s mixture, maize: beans = 4:3

maize =^{Ratio of maize}/_{Total ratio}x No of kg

=4/_{7}x 126

72kg

In Dan’s mixture, maize: beans = 5: 4

Maize =^{Ratio of maize}/_{Total ratio}x No of kg

=^{5}/_{7}x 126

= 70kg

Difference = ( 72 - 70 )kg

= 2kg

The correct answer is A (2kg)

- A rectangular plot measures 12m by 10m.The length of the plot is increased in the ratio 3:2 , while the width is decreased in the ratio 4;5.By what ratio is the area of the plot decreased?
- 4:3
- 5:4
- 6:5
- 3:2

Working

New length after increase^{3}/_{2}x 12 = 18m

New width after decrease^{4}/_{5}x 10 = 8m

Original area before the increase/decrease

= (12 x 10) m^{2}

= 120m^{2}

New area = (18 x 8) m^{2}

= 144 m^{2}

New ratio = 144: 120

= 6 : 5

The correct answer is C (6: 5).

- Gladys keeps hens, ducks, and turkeys. The ratio of hens to ducks is 5:2. The number of turkeys is 35 less than the number of hens. How many turkeys are there if there are 30 ducks?
- 105
- 40
- 75
- 65

Working

Hens : ducks = 5 : 2

Total ratio = 7

Ducks =^{ 2}/_{5}Hens =^{5}/_{7}of x

Therefore^{2}/_{7}of x = 30

x = 30 x^{7}/_{2}x = 105 (Total hens and ducks)

Hens =^{5}/_{7}x 105

= 75

Turkeys = (75 – 35)

The correct answer is B (40)

- Elijah and Paul shared some money in the ratio 5:8.Elijah got sh120 less than Paul. How much money did Paul get?
- Sh520
- Sh320
- Sh200
- Sh192

Working

Let the amount Paul got be t

Therefore Elijah got (t-120)

Therefore t -120 : t = 5 : 8^{t – 120}/_{t}=^{5}/_{8}8t – 960 = 5t

8t – 5t = 960

3t = 960

t = sh320

Therefore Paul got = sh 320

The correct answer is B (sh320)

- A contractor employed 60 men to complete a piece of work in 150 days. How many more days would 50 men take to complete the same work?
- 180
- 30
- 40
- 50

Working

60 men take 150 days

1 man take (150x60) days

Therefore 50 men will take^{150 x 60}/_{50}days

= 180 days

How many more? (180 – 150) days

= 30 days

The correct answer is B (30 days)

- Eighteen men can finish to dig a piece of land in 45 days. How many days would 15 men take to finish the same piece of land?
- 54
- 2
- 7½
- 9

Working

18 men take 45 days

1 man takes (45 x 18) days

Therefore 15 men will take^{ 45 x 18}/_{15}= 54 days

The correct answer is A (54 days)

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