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. 7½
   4. 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)