# Quantitative Aptitude Study Notes on Percentage – Learn Dunia

Percentage Study Notes: The term percent means ‘for every hundred’. If can be defined as: “A fraction whose denominator is 100 is called percentage, and the numerator or the fraction is called the rate per cent.”It is often denoted using the percent sign, “%”.

### Some Important Points on Percentage

1: If two values x% and y% more than a third value, then the first is the  (100+X/100+Y )*100% of the second.

2: If A is x% of C & B is y% of C then, A is (X/Y)*100% of B.

3:   x% of a quantity is taken by the first, y% of the remaining is taken by the second & z% of the remaining is taken by third persons, now, if A is left in the fund, then there was

(A*100*100*100)/(100-x)(100-y)(100-z) in the beginning.

4: x% of a quantity is added. Again y% of the increased quantity is added. Again, z% of the increased quantity is added. Now it becomes A, then the initial amount is given by:

(A*100*100*100)/(100+x)(100+y)(100+z).

5: The Population of a town is P. It increased by x% during the first year, increased y% during the second year and again increased z% during the third year. The population after third year will be.

(p* (100+x)(100+y)(100+z))/100*100*100.

6: When the Population decreases by y% during the second year, while for the first and third year, it follows the same, the population after 3 years will be.

(P*(100+x)(100-y)(100+z))/100*100*100.

7: If the Price of the commodity decreases by r%, then increases in consumption so as not to be decrease expenditure on this item is. [(r)/(100-r)*100]%.

8: If the value of a number is first increased by x% and later decreased by y% the net change is always a decrease which is equal to:

x% of x.

9: If the Value is first increased by x% and the decreased by y% then there is increased or decrease:

(x-y-xy/100)%.

10: If the Value is increased successively by x% and the y% then the final increase is given by:

[x+y+xy/100]%.

11: The Passing marks in an examination is x%, if a candidate who score y marks fail by z marks, then the maximum marks is :

(100(y+z))/x.