**Percentage (Quantitative Aptitude) for Bank PO, Clerk, SSC CHSL, CGL and other competitive exams Increase, Decrease,population formula,successive,dimensional figure,area,fractional equivalent**

**Percentage**

**•**A percentage is a fraction with denominator hundred.

To convert any fraction a/b to rate percentage multiply it by 100 and put % sign.

* Percentage increase or decrease = Increase or Decrease

**/**base value ×100

• If A is r % more than B,then A by r

**/**100+r×100

• If A is r % less than A by r

**/**100-r×100
These formula are also used for consumption

**Population formula**

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^{• }If the annual decrease be r % then the population after n year is p (1-r/100)

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**First increase and then decrease**

**•**If the value is first increased by x % and the decreased by y % then there is (x-y-xy/100)% increase according to the +ve or -ve sign respectively.

• If the value is first increased by x% and then decreased by x% then there is only decrease which is equal to (x

*Average percentage rate of change over a period.

(New value - old value )×100/n%. where n = period.

The percentage error = The error

^{2}/100).*Average percentage rate of change over a period.

(New value - old value )×100/n%. where n = period.

The percentage error = The error

**/**True value**Successive increase or decrease****If the value is increased successively by x% and y% then the final increase is given by (x+y+xy/100)%**

**Student and Marks****• The percentage of passing marks in an examination is x%. If a candidate who scores y then the maximum marks m = 100(y+z)/x.**

• A candidate scoring x% in an examination fails by 'a' marks while another candidate who scores y% marks get 'b'marks more than the minimum required passing marks. Then the maximum marks m = 100(a+b)/y-x

In an examination x % and y % student respectively fail in two different subjects while z % students fail in both subjects. Then the % age of student who pass in both the subject will be 100-(x+y-z)%

**2 - Dimensional figure and area**

**•**If the sides of a triangle,square,rectangle,rhombus or rhombus or radius of a circle are increased by a % its area is increased by a (a+200)%/100.

• If the sides of a triangle , square , rectangle , rhombus or radius of a % then its area is decreased by a (200-a)/100%.

• If A's income is r % more than that of B, income is less than that of A by (

*r*/100+r×100)%.
• If A's income is r % less than that of B,then B's income is more than that of A by (r/100-r×100)%.

**Fractional Equivalent of %**

**•**1% = 1/100

• 2% = 1/50

• 4% = 1/25

• 5% = 1/20

• 10% = 1/10

• 16% = 4/25

• 20% = 1/5

• 25% = 1/4

• 40% = 2/5

• 50% = 1/2

• 60% = 3/5

• 75% = 3/4

• 80% = 4/5

• 90% = 24/25

• 100% = 1

• 115% = 23/24

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