**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, “%”.

**Percentage Chart**

**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.**

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