Ratio and Proportions

RATIO AND PROPORTIONS

The number of times one quantity contains another quantity of the same kind is called the Ratio of the two quantities.

The ratio 2 to 3 is written as 2:3 or . 2 and 3 are called the terms of the ratio. 2 is the first terms (is also called antecedent) and 3 is the second term (is also called consequent).

COMPOUND RATIO

Ratios are compounded by multiplying together the antecedents for a new antecedent, and the consequents for a new consequent.

                                                                                                     a x c x e

·         Ratios  a:b,c:d, and e:f      Compounded of the four ratios :------------

                                                                                        b x d x f

a.       Find the ratio compounded of the four ratios:

                                                                 
4:3, 9:13, 26:5 and 2:15                      ans is 16/25

When the ratio 4:3 is compounded with itself, the resulting ratio is 4²:3². It is called Duplicate Ratio of 4:3.

Similarly, 4³:3³ is Triplicate ratio of 4:3

√4: √3 is called the subduplicate ratio of 4:3

·         ABC are three quantities of the same kind such that A:B=2:3,B:C=4:5,

                                                              i.      Find the ratio of A:C

                                                            ii.      Find A:B:C and

A : B                            2 : 3

                  B : C                           4 : 5

            ---------------                 -----------

            AB:BB:BC                 2x4:3x4:3x5

                                                8   :12 : 15      

            Ans i. 8:15

                  ii. 8:12:15

           

            Practice below problems

a.       A:B=3:5,B:C=2:3 Find the values of A:B:C                 Ans. 6:10:15

b.      A:B=5:3,B:C=7:4 Find the values of A:B:C                 Ans. 35:21:12

c.       a=2/3b, b=4/5c Find the values of a:b:c                                Ans. 8:12:15
           a/b=2/3  b/c=4/5

d.      P=3/5Q Q=2/3R Find the values of P:Q:R                             Ans.6:10:15

e.       2a=3b, 4b=5c Find the values of a:b:c                         Ans.15:10:8

a:b=3:2            b:c=5:4

f.       2a = 3b = 4c Find the values of a:b:c                           Ans.12:8:6

a:b=3:2            b:c=4:3

g.       x=3y=5z  Find the values of x:y:z                               Ans.15:5:3

·         The sum of three numbers is 98. If the ratio between the a:b= 2:3 and the b:c=5:8, then find the value of ‘b’.

2 : 3

    5 : 8

                        -----------

                        10 : 15 : 24

                                                   98

            The second number = ------------  x 15=30

                                  10+15+24

Practice below problems

a.       The ratio of the money with Rita and Sita is 7:15 and that with Sita and Kavita is 7:16. If Rita has Rs 490, how much money does Kavita have?  Ans. Rs.2400

·         ABCD are four quantities of the same kind such that A:B=3:4,B:C=8:9,C:D=15:16,

                                                          iii.      Find the ratio of A:D

                                                          iv.      Find A:B:C and

                                                            v.      Find A:B:C:D

  

A : B                                        3 : 4

     B : C                                        8 : 9

            C : D                                     15 : 16

------------------                          ----------------

ABC:BBC:BCC:BCD               360:480:540:576

Practice below problems

a.       A:B=2:3,B:C=4:5 C:D=3:2 Find the values of A:B:C:D     Ans. 24:36:45:30

b.      P:Q=3:5,Q:R=2:1, R:S=2:3 Find the values of P:Q:R:S       Ans. 12:20:10:15