Ratio and Proportion kya hai

RATIO: The symbol of ratio is (:). So, a ratio b is written as a : b or  a/b. The first term of ratio is called antecedent and the 2nd term is called consequent.

PROPORTION: Proportion is the same of ratio and is denoted by the symbol ''::'' . So if a : b and c : d are equal then it is written as
a : b :: c : d .
INVERSE RATIO: If a : b is any ratio, then (1/a : 1/b) is called inverse or reciprocal ratio.
COMPLEX RATIO: The product of the first term of two or more than two ratio, and product of their last term and ratio of these two products is called complex ratio.i.e., a : b, c : d, c : f. So, complex ratio will be ( a x c x e ) : ( b x d x f ).

IMPORTANT FORMULAE:-

• If a : b :: c : d =>  a/b = c/d => a x d = b x d.
• If fourth proportional of three numbers a, b and c is 'd' then a : b :: c : d => a x d = b x c => d = (bc/a).
• If third proportional of two numbers a and b is c, then a : b :: b : c => a x c = b^2 => c =( b^2/a ).
• The mixed ratio of two ratios ( a : b ) and ( c : d ) is ( ac : bd ).
• If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d).
• The reciprocal ratio of a, b, c is = 1/a : 1/b : 1/c = bc : ca : ab.