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Sunday, 13 August 2017

Important Notes : Ratio And Proportion

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 Important Notes : Ratio And Proportion




RATIO AND PROPORTIONS 

Ratio: Ratio is the comparison of two quantities. The ratio of ‘A’ to ‘B’ is written as

                        A : B = 2 : 3

                  ๐‘จ/๐‘ฉ  = ๐Ÿ/๐Ÿ‘

CONCEPT OF PROPORTION


Proportion:  A proportion is an expression which states that two ratios are equal.

ratio proportion  =  ratio proportion  is a proportion


TYPE OF PROPORTION


If  A, B, and C are in proportion.

 e.g.

            A : B :: B : C
            Important Notes : Ratio And Proportion




MEAN PROPORTION 

 Important Notes : Ratio And Proportion
B2  =  ratio proportion
  B   =  ratio proportion

THIRD PROPORTION 

 Important Notes : Ratio And Proportion

ratio proportion
FOURTH PROPORTION 

If four quantities A, B, C and D are in proportion 

                     So,            A : B : : C : D 

                                           Important Notes : Ratio And Proportion
                             
ratio proportion
Ex:    If A and B are in the ratio 4:5 and the difference of their squares is 81, what is the value of A.

Sol:  
ratio proportion
ratio proportion
 x = 3
So A = 3 × 4 = 12

Ex:    Two alloys contain tin and iron in the ratio of 1:2 and 2:3. If the two alloys are mixed in the proportion of 3:4 respectively (by weight), the ratio of tin and iron in the newly formed alloys is.

          Ist Alloy suppose 3× 3 = 9kg and IInd alloy  5 × 4 = 20
               3  6               
          8        12             
          11   : 22
                    1  :   2

 Ex: In a bag 240 coins of 50 paise, 25 paise and 10 paise and their value are in the 5 :3 : 1 then finds the number of 25 paise coins.

ratio proportion
ratio proportion
                    = 5 : 6 : 5
25 paise coins = ratio proportion × 6 = 90

Ex: Price of a piece of a diamond changes according to the square of its weight. If a diamonds of Rs 5184 is cut in three parts in such a way that weight of parts in such a way that weight of these parts in the ratio 1 : 2 : 3 , then find the amount of loss by cutting the diamond.

ratio proportion

x2 = 5184
x = 72
Ratio of the part of the diamond = 1: 2 : 3
Weight of parts   = 12 , 24 , 36
Total value = 122 + 242 + 362  
                   = 2016
Loss = 5184 – 2016 = 3168

Ex: Three persons A, B, C whose salaries together amount to Rs 72000 spend 80, 85 and 75 percent of their salaries respectively. If their savings are in the ratio 8 : 9 : 20, then A's salaries is-

Sol:  

If the salaries of A, B and C be Rs. x, Rs. y and Rs. z respectively then
ratio proportion
x:y:z = 40 : 60 : 80
= 2 : 3 : 4
A's salary =
ratio proportionRs.

Ex:    The ratio of the first and second class fares between two railway stations is 4 : 1 and that of the number of passengers travelling by first and second classes is 1 : 40. If on a day Rs. 1100 are collected as total fare, the amount collected from the first class passenger is.
Sol:   Ratio of the first and second class fares (total)
=1× 4 : 1 × 40
= 4 : 40 = 1 : 10
  • Amount collected from the first class passengers
ratio proportion        
Ex:    What least number must be subtracted from each of the numbers 14, 17 , 34 and 42 so that the remainders may be proportional?

          Sol:   Let the required number be x.
                   Then, (14 – x) : (17 – x) :: (34 – x) : (42 – x)
                   ratio proportion
                   ratio proportion
                    ratio proportionx2 – 56x + 588 = x2 – 51x + 578
                    ratio proportion5x = 10 ratio proportion
                   Required number = 2

Ex:  Seats for Mathematics, Physics, and Biology in a college are in the ratio of 5 : 7 : 8 . There is a proposal to increase these seats by 40%, 50%, and 75% respectively.What will be the ratio of seats after increase?

Sol:
          Initial ratio = 5 : 7 : 8

     After increase = 5 ratio proportion : 7ratio proportion : 8ratio proportion

                              = 2 : 3 : 4

Ex:   A, B and C have 40, X and Y stones with them respectively. If B gives 20 stones to A , he is left with half as many stones as C. If together they had 60 more stones, each of them would have had 100 stones on an average. What is the value of X : Y ? 
Sol :
              ratio proportion =100
                    X + Y = 200 -------(1)
                      ratio proportion = ratio proportion
                   2X – Y = 40 --------(2)
   From both the eq.
      X = 80 , Y = 120
             X : Y = 2 : 3

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