Paper 4: Fundamentals of Business Mathematics & Statistic

Study Note - 1

ARITHMETIC

1.1 RATIO AND PROPORTION

1.1.1 Ratio
The ratio between quantities a and b of same kind is obtained by dividing a by b and is denoted by a : b.
Inverse Ratio: For the ratio a : b inverse ratio is b : a.
A ratio remains unaltered if its terms are multiplied or divided by the same number.
a : b = am : bm (multiplied by m)

a : b =m ma b: (divided by m ≠ 0)

Thus 2 : 3 = 2 x 2 : 3 x 2 = 4 : 6 =4 62 2: = 2 : 3
If a = b, the ratio a : b is known as ratio of equality.
If a > b, then ratio a : b is known as ratio of greater inequality i.e. 7 : 4 And for a < b, ratio a : b will be the
ratio of Lesser inequality i.e. 4 : 7.
Solved Examples:
Example 1 : Reduce the two quantities in same unit.
If a = 2kg., b = 400gm, then a : b = 2000 : 400 = 20 : 4 = 5 : 1 (here kg is changed to gm)
Example 2 : If a quantity increases by a given ratio, multiply the quantity by the greater ratio.
If price of crude oil increased by 4 : 5, which was 20 per unit of then present price = 20 ×^54 = 25 per unit.
Example 3 : If again a quantity decreases by a given ratio, then multiply the quantity by the lesser ratio.
In the above example of the price of oil is decreased by 4 : 3, the present price =^20 ×^34
= ` 15 per unit.
If both increase and decrease of a quantity are present is a problem, then multiply the quantity by greater
ratio for increase and lesser ratio for decrease, to obtain the final result.
1.1.2 Proportion
An equation that equates two ratios is a proportion. For instance, if the ratio
a
b is equal to the ratio

c

then the following proportion can be written: d,

Means

=

Extremes

a

b

c

d

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 1.

This Study Note includes

1.1 Ratio & Proportion

1.2 Simple & Compound Interest (Including Application of Annuity)

1.3 Discounting of Bills & Average Due Date

1.4 Mathematical Reasoning - Basic Application