Ratios and proportions

Introduction:

• The ratio of numbers A and B can be expressed as the ratio of A to B.
• The numbers A and B are sometimes called terms with A being the antecedent and B being the consequent.
• The proportion expressing the equality of the ratios A:B and C:D is written A:B = C:D or A:B::C:D. 

• A, B, C and D are called the terms of the proportion. A and D are called the extremes, and B and C are called the means. The equality of three or more proportions is called a continued proportion.

•  Product of extremes = Product of Means
  To solve proportion, we use above principal, A single term in the proportion is called proportional.

  “a” is the 1st proportional.
  “b” is the 2nd proportional.
  “c” is the 3rd proportional.
  “d” is the 4th proportional.1

• EX:Find the third proportional in 3:2=x:8 ?
• sol;product of extremes = product of means

                      2x = 16     

         Points to remember:

•  1/a:1/b =b:a
• 1/a:1/b:1/c=bc:ac:ab

Exercise problems:
1)the two terms are in the ratio  5:7.the sum of the two terms are 108. find the two numbers?
 a)
      let the two numbers are 5x,7x.
sum of the two numbers are 5x+7x=108
                                              12x=108
                                                 x=9
                       1  part   = 9
                      5   part's = 5*9 = 45
                      7 part.s=  7*9  =63

2)the length and breadth of rectangle are in the ratio of 9:5. the length exceeds the breadth by 280 meters.find the perimeter of the rectangle?
a)           l:b    =    9:5
            l-b=9-5=4
    in the question the 4  part is given as 280.
                       1 part =  70
                        length=9*70=630 meters
                       breadth=5*70=350 meters
                       perimeter=2(l+b)=  2(630+350)
                                                 =1960

3) If a sum of Rs.11400 is divide among A,B and C in the ratio of 3:4:5. find the share of  C?
 a)  
      A:B:C=  3:4:5
    let  the share of A,B and C are 3x,4x,5x,respectively
             3x+4x+5x     =  11400
                        12x    = 11400
                          x     =  950
the share of c is 5*950=4750.

4)The two numbers are in the  ratio 17:18 .when 8 is added to both the numbers the ratio becomes 19:20.
Find the smaller number?
A)
        let the numbers be   A:B=  17:18
     when 8 is added the new ratio becomes A:B=19:20      

the change in the ratio is 2 .So     2 parts =8
                                                 1 part  = 4
                                  the smallest number is 17*4=68.

5) If a sum of Rs. 2460 is divided  among A,B and C such that A gets 7/6 of what B gets and B gets 4/5 of what C gets .find the share of B?
A)
        A=7/6 B
        B=4/5 c
     
        A:B      =  7 : 6
            B:C  =      4 : 5
      A : B: C = 14:12:15.
the trick is very simple. take the L.C.M of 6 and 4 is 12.
    write the 12 in place of B
multiply 7 with 2 because to get 12 ,6 is multiplied with 2 and multiply 5 with 3.
the A:B:C   =  14:12:15
       41x=2460
          x= 60
the share of B is 12x=12*60=720