Wednesday, 15 September 2021 09:20

## Ratio And Proportion - Class 8 Mathematics Revision Notes

### Ratio And Proportion

Worked Exercise

1. 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?
1. 2
2. 3
3. 4
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)
2. 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?
1. 4:3
2. 5:4
3. 6:5
4. 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) m2
= 120m2
New area = (18 x 8) m2
= 144 m2
New ratio = 144: 120
= 6 : 5
The correct answer is C (6: 5).
3. 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?
1. 105
2. 40
3. 75
4. 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)
4. Elijah and Paul shared some money in the ratio 5:8.Elijah got sh120 less than Paul. How much money did Paul get?
1. Sh520
2. Sh320
3. Sh200
4. 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)
5. 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?
1. 180
2. 30
3. 40
4. 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)
6. 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?
1. 54
2. 2
3. 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)