Quant Study Notes: Percentage

All about Percentage

Percentage means per hundred when we say 50% of a number it means half of the number. Similarly, 25% of a number is one fourth of the number; 20% means one fifth of the number, 16.67% means one sixth of a number etc. Hence percentage indicates the part or fraction of a number.

Percentage and Ratio

Following table gives equivalence relation between commonly used fractions and their equivalent percentages

Some times using fractions is better than using actual percentage. ☞For example to calculate 14.28% of 343, we should not directly use multiplication, we can use equivalent fractions of 14.28% i.e. 1/7 hence the required answer

Example: Calculate 30% of 710

Method 2:-
In this method we will learn a different approach.
Any number is always 100% of itself
So the 100% of 710 is    = 710
10% of 710 is         = 71.0
1% of 710 is         = 7.10
0.1% of 710 is         = 0.710
We require 30% of 710, which is = 3 × 10% of 710
= 3 ×71 = 213
Successive Increment/Decrement ☞Suppose a number is increased or decrease by x% then by y%, if the initial value of the number is n, then it’s final value

☞Alternatively, we can use the successive change formula,
Effective percentage increase or decrease

☞If a quantity changes by three consecutive changes of x%, y% and z%, then the effective percentage change

Percentage Points
Percentage point is used to simplify the data in percentage point and it is defined as difference of two percentage figures for example if a man spends 10% of his salary in the month of January and 25% in the month of February, then we can say that expenditure increases by 15 percentage point and percentage increase is:

(Assuming that his salary remains constant)
Example:
A mixture of 40 liters of milk and water contains 10% water. How much water should be added to it so that water may be 20% in the new mixture?