__CHAPTER-3__

__PERCENTAGE__

__What is percentage?__

Percentage is a fraction or a numerical expression or a ration with 100 assumed as denominator. So we can represent 1 percentage as 1%.

Points to be remember-

**1 = 100%****1/2 = 50%****1/3 = 33****%****1/4 = 25%****1/5 = 20%****1/6 = 16****%****1/7 = 14****%****1/8 = 12****%****1/9 = 11****%****1/10 = 10%****1/11 = 9****%****1/12 = 8****%****1/13 = 7****%**- If the price of a commodity increases by R%,then the reduction in consumption as not to increase the expenditure is =
**%** - If the price of a commodity decreases by R%,then the increase in consumption as not to decrease the expenditure is=
**.**

- Let the population of a town be P now and suppose it increases at the rate of R% per annul, then:
- Population after n years =
**P (1+R/100)**^{n} - Population n years ago =
- Let the present value of a machine be
**P**. Suppose it depreciates at the rate of**R%**per annul, then : - Value of the machine after
**n**years =**P(1-R/100)**^{n} - Value of the machine
**n**years ago = - If
**A**is**R%**more than**B**, then**B**is less than**A**by=**%** - If
**A**is**R%**less than**B**, then**B**is more than**A**by= %**.**

__Percentage Type1 Shortcut Tricks__

__Example:__

If the difference between 45% of a number and 3/5th of that number is 18. What is the number?

__Solution:__

Let the number be a .

Then a x 45% – a x 3/5 = 18

a x 45% – a x 60% = 18 ∴( 60% = 3/5 )

a x 15% =18

a = 100×18 = 1800/15 = 120

__Tricks:__

we know 3/5 = 30%

45% – 30% = 15 %

15% = 18 = 120

__Percentage Type2 Shortcut Tricks__

__Example:__

Sahil work in shop and his 30% of income is Rs.1800 .Find the 65% of his income and also find the 1 / 5 of Sahil’sincome.

**Solution:**30%**= 1800 So,**65% = 1800 x 65 / 30 = 3900**Shortcut Trick:**1800 x 65 / 30 = 3900.

__Example:__

Raj spend his money from his saving in different way that is he spends 30% on travel,10% on food,15% on wages and 22% on purchase a bike and after that all expenditure he saved 4600.Find the how much he spent on bike.

**Solution: **Let the total income of Raj=X.

then total expenditure from income = X x (30%+10%+15%+22%)=>X x 77%

Total savings= X x 23%

**X = 4600 x 100 / 23 = 20000 and expenditure on Bike = 22% so, 20000 x 22 / 100 = 4400.**

**Shortcut Tricks**

The total income as 100% so, (100% – 30%+10%+15%+22%) = 77% and now (100% – 77%) = 23%

**Bike Expenditure is now 4600 x 22 / 23 = 4400.**

__Example:__

Sanjay got 88 marks in Hindi , 81 marks in Science , 74 marks in Maths , 68 marks in Social Science and 57 marks in History . The maximum marks of each subject are100. How much overall percentage of marks did he get?

**Solution:**** Percentage = 368 x 100 / 500 = 73.6**