Ratio,Proportion,Partnership and Mixture

 

 Ratio,Proportion,Partnership and Mixture

Ratio :-
       Ratio compares two or more quantities of same kind with each other by method of division.It is a relation that one quantity bears to another with respect to magnitude or in other words, ratio of two quantities is the number of times of one quantity contains another quantities of same kind.
       If a and b are two quantities of the same kind,then a/b known  as the ratio of a and b . It is clear that ,the ratio of two quantities is equivalent to the fraction of one quantities to the other.
       Thus , a to b is the ratio (a/b) , written as a:b.
   
     The first term of the ratio is called antecedent while the second term is called consequent.
    
     A ratio remains unchanged . if each term of a ratio are multiplied or divided by the same number.

Classification of Ratio:-
  1.      Duplicate ratio:- a2:b2 is called duplicate ratio of a:b.
  2.      Triplicate ratio:- a3:b3 is called triplicate ratio of a:b. 
  3.      Subduplicate ratio :- √a:√b is called subduplicate ratio of a:b.
  4.      Subtriplicate ratio:-∛a:∛b is called subtriplicate ratio of a:b.
  5.      Compound ratio:-  ab:cd is called the compound ratio of a:c and b:d. It is the ratio of the product of the ant;ecedents to that of the consequents of the two or more given ratios.
  6. Inverse Ratio:- 1⁄a:1⁄b is the inverse ratio of a:b.
Relation among More Than Two Quantities :-
             1.  For three quantities : If A : B = x1 : y1 and B : C = x2 : y2, 
                    then the ratio of A : B : C = (x1 × x2) : (y1 × x2) : (y1 × y2)
             2.  For four quantities : If A : B = N : D, B : C = N : D and C : D = N : D
                     then A : B : C = N1 N2 N3 : D1 N2 N3 : D1 D2 N3 : D1 D2 D3 

Proportion 

    The equality of two ratios is called proportion. a,b,c and d are said to be is proportion,if a : b = c : d . Here a is the first term , b is the second term , c is the third term and d is fourth term. Here, first and fourth terms are called extremes i.e. a and d , while the second and third terms are called as means i.e. b and c .
 e.g. If 3 : 2 : : 135 : 90 then 3 and 90 are called the extremes, while 2 and 135 are called the means. 
   In a proportion,  we always have.
  Product of extremes = product of means 
              a : b :: c : d => a × d = b × c

Classification of Proportion :-
  Proportion is divided  types:

       1. Continued proportion :-  If three quantities a,b and c are such that a : b :: b : c ,then b2 = ac and a,b, and c are in continued proportion. Also ,the quantity c is called the third proportion of a and b.

       2.Mean Proportion:-   if three quantities a ,b and x are such  a : x :: x : b , then  x = ab and x is called the mean proportions of a and b.
                                                 x = √ab
       3. Fourth proportion:- if four quantities a,b,c and x are such that a : b :: c : x,then ax = bc and x is called the fourth proportion of a , b and c.
  • Invertendo  :- if a : b :: c : d ,then b : a :: d : c 
  • Alternendo  :- if a: b :: c : d , then a : c :: b : d
  • Componendo :- if a : b :: c : d ,then (a+b) : b :: (c+d) : d.
  • Dividendo :- if a : b :: c : d ,then (a-b) : b :: (c-d) : d
  • Componendo-dividendo :- if a : b :: c : d ,then (a+b) : (a-b) :: (c+d) : (c-d)

ELEMENTARY FORMULAE ON PARTNERSHIP

   The ratio of profits p1 and p2 in any partnership is equal to the ratio of product of investment x1 and x2 with the time period of investment t1 and t2 respectively.
                    p1 × p2 = x1 × t1 : x2 × t2 
  

SOLVED EXAMPLE 








Here is PDF of above solved problem
download (Click Here)

more practice problem on this topic
download (Click Here)

solution of practice sheets is 
download(Click Here)

Comments

Post a Comment

Popular posts from this blog

Simple and compound Interest

Image
Simple and compound Interest Simple Interest:- Basic formulae for calculation of various parameters related to simple interest  are explained as under If P= Principal, R = Rate per cent per annum ,T= Number of years, SI = Simple interest and A = Amount, Then Elementary Formulae on Simple Interest 1.Change of rate of interest and time when interest is calculated for different specified time.    if original rate = R% and time  = T yr , Then    For half-yearly, rate = R/2 % and time = 2T    For quarterly, rate = R/4 % and time = 4T    For quarterly, rate = R/12 % and time =12T 2. When a sum becomes n times of its in T yr at a rate of R% per annum, then RT = (n-1) x 100 3. When the simple interest on a sum at R% per annum in T yr is X/Y of the sum, then for R = T       T = R = √ [(x/y) x 100 ] 4. When two equal sum are deposited for T 1 and T 2 at the rate of interest of R 1 % and R ...
Read more

permutation and combination

Image
Permutation and Combination permutation and combination are ways for the arrangement or selection of a group of persons/ numbers etc. Permutation is an act of rearrangement all the members of a set into same sequence or order.It is one of the different arrangement of a group of items where order / sequence / way matters whereas combination is a way of selecting members from the group such that the order of selection doesn't matter. Fundamental principle of multiplication  It there are two jobs such that one of them can be completed in m ways and second job can be completed in m ×n ways. e.g. If there are 4 ways in which a person can go from X to Y and 7 ways in which he can go from Y to Z , then possible ways to go from X to Z = 4 ×7 = 28 ways. Fundamental principle of addition If there two jobs such that they can be performed independently in m and n ways respectively , then either of the two jobs performed in (m+n) ways. Permutation By permutation we mean...
Read more

Probability

Image
Probability Probability is just the chance of happening of an event . In other words , Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence which is expressed as a number between 1 and 0.  e.g.  The probability of a coin toss resulting in head is 1/2. The probability is defined as the chance of happening or not happening of an event. Important terms Related to probability : * Experiment  An action which result in some well-defined outcomes . * Random experiment  A random experiment is an experiment or a process for which the outcomes cannot be predicted with certainity .    Whenever an experiment is conducted a number of times under similar condition where the resultis not certain , then the experiment is called a trial or a random experiment , the outcomes are known as events. e.g. When a die is thrown , it is a trial , getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event. *...
Read more