Paper 4: Fundamentals of Business Mathematics & Statistic

1.2 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Arithmetic

The numbers a and d are the extremes of the proportion. The numbers b and c are the means of the

proportion.

Properties of proportions

1. Cross product property: The product of the extremes equals the product of the means.
   If b da c= , then ad = bc.


2. Reciprocal property: If two ratios are equal, then their reciprocals are also equal.
   If a cb d= , then b da c=.

Few Terms :

1. Continued proportions : The quantities a, b, c, d, e.... are said to be in continued proportion of a : b =
   b :c = c .... Thus 1, 3, 9, 27, 81, ..... are in continued proportion as 1 : 3 = 3 : 9 = 9 : 27 = 27 : 81 = ....
   Say for example : If 2, x and 18 are in continued proportion, find x. Now 2 : x = x : 18 or,
   2 x or,x 36 or,x 6 2
   x 18= = = ±
   Observation: If a, b, c are in continued proportion, the b ac, b^2 = = ± ac.


2. Compound Proportion : If two or more ratios are multiplied together then they are known as
   compounded.
   Thus a 1 a 2 a 3 : b 1 b 2 b 3 is a compounded ratios of the ratios a 1 : b 1 ; a 2 : b 2 and a 3 : b 3. This method is also
   known as compound rule of three.
   Example 4 : 10 men working 8 hours a day can finish a work in 12 days. In how many days can 12 men
   working 5 hours a day finish the same work.?
   Men Hours day
   Arrangement : 10 8 12
   12 5 x

x 12 8 10 16 days

= ×5 12× =

Observation : less working hour means more working days, so multiply by greater ratio^85. Again more

men means less number of days, so multiply by lesser ratio^1012.

Derived Proportion : Given quantities a, b, c, d are in proportion.

(i) Invertendo : If a : b = c : d then b : a = d : c

(ii) Alternendo : If a : b = c : d, then a : c = b : d

(iii) Componendo and Dividendo

If a cb d= thena b c da b c d+− = +−