## Percentage formulas | percentage calculations with examples

Contents

*Percentage calculation* is one of the important part in mathematics. *Percentage formulas* very helpful to all competitive exams as well as in our daily life. In this artical provides different types of formulas for percentage calculation with examples.

### Type 1 : General Percent formulas.

Find X is what percent on Y ?

X is what percent greater than Y ?

is what percent lesser than Y ?

__Examples for the above percentage formulas__

Ex. 1 : 25 is what percent on 40 ?

solution : (25/40) x 100 = 62.5%

Ex. 2 : 25 is what percent less than 40 ?

solution : [(40-25)/40] x 100 = 37.5%

Ex. 3 : 50 is what percent greater than 40 ?

solution : [(50-40)/40] x 100 = 25%

### Type 2 : Net change of a number while percentage increase or decrease.

Net change of a number while increased by and then again increased by Y.

Net change of a number while decreased by and then again decreased by Y.

The Net change of a number while increased by and then again decreased by Y.

Net change of a number while decreased by and then again increased by Y.

**Hints:**

- Increase means ” + ” sign and decreased means ” – ” sign . If net change is positive, it means final value increased. If net change is negative, it means final value decreased.
- A number increases by x and then again decreases by , (i.e same percent) then, net value always decreases by
**(x / 10)**^{2} - If a number decreases by x and then again increases by , (i.e same percent) then, net value always decreases by
**(x / 10)**^{2}

__Examples for the above percentage formulas__

Ex.1 : Find the net percent change of a number while it is increased by 20 and then again increased by 1

Solution : 20 + 10 + ( 20 x 10 /100) = 32% increased.

Ex.2 : Find the net value of a number ” 60 “while it is increased by 25 and then again decreased by 15

Solution : 25 – 15 – (25 x 15/100) = 25 – 15 – 3.75 = 6.25 % ( increased )

= 60 + (60 x 6.25 %) = 60 + [ 60 x (6.25/100)] = 60 + 3.75 = 63.75.

Ex.3 : Find the net value of a number ” 240 “while it is decreased by 30 and then again increased by 10

Solution : -30 + 10 – (30 x 10/100) = – 30 + 10 – 3 = – 23 % ( decreased )

= 240 – (240 x 23 %) = 240 – [ 240 x (23/100)] = 240 – 55.2 = 184.8.

Ex.4 : Find the net percent change of a number while it is decreased by 20 and then again decreased by 30

Solution : – 20 – 30 + ( 20 x 30 /100) = -20 – 30 + 6% = -44% (decreased).

Ex.5 : Find the net change in revenue, If price of a commodity decreases by and again its price increases by

Solution : – 10 + 20 – (10 x 20/100) = -10 + 20 -2 = 8 %

The final price of the commodity increased by 8%.

Ex.6 : Find the net change in revenue, If price of a commodity decreases by and again its price increases by 1

Solution : (15 / 10)^{2} = 2.25 %

The final price of the commodity decreased by 2.25%.

### Type 3 : Net percent change in area of circle or square

If radius of a circle is increased by , then its area is increased by

If radius of a circle is decreased by , then its area is decreased by

__Examples for the above percentage formulas__

Ex.1 : Find the net change in area of a circle , If radius of the circle decreases by and again its radius increases by 10

Solution : – 20 + 10 – [(20 x 10) / 100)] = -10 – 2 = -12% ( i.e radius decreased by 12% so change in radius 1- 0.12 = 0.88)

Area = π x r^{2} = π x (0.88 r)^{2} = 0.7744 x π x r^{2}

So Area of the circle decreased by 100- 77.44 = 22.56%

Ex.2 : Find the net change in area of a circle , If radius of the circle increases by and again decreases by 10

Solution : 30 – 10 – [(30 x 10) / 100)] = 20 – 3 = -17% ( i.e radius increased by 17% so change in radius 1+0.17 = 1.17)

Area = π x r^{2} = π x (1.17 r)^{2} = 1.3689 x π x r^{2}

So Area of the circle increased by 136.89 – 100 = 36.89%

Ex.3 : Find the net change in area of a square , If side of the square increases by .

Solution : (2 x 30) + (30 x 30 /100) = 60 + 9 = 69%

So Area of the square increased by 69%

Ex.4 : Find the net change in area of a circle , If radius of the circle decreases by .

Solution : – (2 x 18) + (18 x 18 /100) = – 36 +3.24 = – 32.73%.

So Area of the circle increased by 32.73%.

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## 2 thoughts on “Percentage formulas while increase and decrease percent of a number”

## Cube Root formula of Perfect Cubes of 1 to 100 | Cube root formula in math

(October 12, 2017 - 5:00 pm)[…] Percentage formulas while increase and decrease percent of a number […]

## Shortcuts for Multiplication of numbers | Easy way for Multiplications

(January 31, 2018 - 4:17 pm)[…] Percentage formulas while increase and decrease percent of a number […]