text: Aptitude Chapter-11
  
  Bodhak competitive bank exam ratio proportion this tutorial is useful to prepare for Bank Exams, Groups Exams, Interviews of MNC & Exams like CRT, CAT, MAT, GRE, GATE  etc. in this chapter we will discuss RATIO AND PROPORTION. We will see how o solve through equations and through shortcut methods.
  
  RATIO AND PROPORTION:
  
  Ratio: The comparison of two similar quantities.
  
  Proportion: The equality of two ratios.
  
  A:B=C:D then D is forth proportion.
  
  A:B=B:C then C is third proportion.
  
  competitive bank exam ratio proportion
  
  A:B=C:D then D is called forth proportion.
  
  A:B=B:C then C is third proportion.
  
  The duplicate ratio of A, B is:  a^2: b^2
  
  The sub duplicate ratio of A,B is      :  sqrt(a) : sqrt(b)
  
  The mean proportion of A, B is: sqrt(ab)
  
  The triplicate ratio of a,b is:a^3: b^3
  
  The fourth proportional to 9,12,36  is?
  
  Solution:
  
  A:B  =C:D Then D is called fourth proportional
  
  A=9,  B=12,  C=36,  D=?
  
  9:12  =  36:D
  
  (9/12)=(36/D)=(1/12)=(4/D)
  
  D  =  12×4  =  48
  
  Find the third proportional to 8,20?
  
  Solution:
  
  A:B  =  B:C then C is called third proportional
  
  A=8,  B=20,  C=?
  
  8:20  =  20:C
  
  c=50
  
  Example:
  
  A sum of money is distributed among A,B,C, D in the proportion of 8:10:7:5. if A gets rs.1500 more then D then C Share is?
  
  Solution:
  
  A:B:C:D  =  8:10:7:5
  
  A=8, D=5
  
  8-5=1500
  
  3=1500
  
  1=500
  
  C=7  =  7×500  =  3500
  
  Example:
  
  Two numbers are in the ratio 1:2. If 7 is added to both the ratio 3:5. The lowest number is?
  
  Solution:
  
  Two numbers are in the 1:2
  
  So one number   =x
  
  another number   =2x
  
  Add 7 to both numbers
  
  (x+7)/(2x+7)=3/5
  
  5(x+7)  =  3(2x+7)
  
  5x+35  =  6x+21
  
  6x-5x  =  35-21
  
  X=14  2x  =  2X14  =  28     So lowest number is 14