Mathematics

Sahana.Bhagavathi

Topic Percentage And Its Applications

TO GAIN KNOWLEDGE AND UNDERSTAND THE USES OF PERCENTAGES,WHERE THEY ARE USED AND SOME EASY TIPS OF PERCENTAGE

Objective

IntroductionThe word per cent is an abbreviation of the Latin phrase means per hundred or

hundredths.The term percent means per hundred or every hundred .When we say that a man gives 30 percent of his income tax, this means he gives ₨30 out of every hundred rupees out of income. ‘A trader

makes 15 per cent a profit in his finial selling’ that means he got a profit of

rupees Rs 15 out hundred.

The symbol % is used for the term percent. So, that means ,7 out of

hundred =7/100

Basics

• A fraction with its denominator 100 is equal to that percent ,as numerator.

• Percent means for every hundred.• Increase%=(Increase x100) Original valueDecrease%=(Decrease/Original value x100) The selling price is written as S.PThe cost price is written as C.P

The effective cost Prices are written as E.C.P

Effective Cost prices (E.C.P)=C.P+overhead expenses

Gain or loss is calculated on the cost price.

Gain%=(Gain /C.PX100)Loss %=(Loss/C.PX100)

Logics

• A fraction with its denominator 100 is equal to that percent ,as the numerator.

• To convert a ratio to a percent,we write it as a fraction ,then multiply the % after the product.

• In a percent 100/100 means whole .• To convert a decimal to a percent we multiply

by 100%.

Loss=C.P-S.PS.P=C.P-Loss

S.P=Profit =C.P

The amount or the price at which an article is purchased by shopkeeper is

cost price(C.P)The amount or price at which an article

is sold by the shopkeeper is called as selling price(S.P).

There are some formulas th find the C.P and S.P:

Profit +S.P-C.P

Theory • ❶To convert a per cent into a fraction, we drop the

per cent and divide the remaining number by hundred. We reduce it to the fracton to the lowest terms. Ex:32% of 80=32/80=4/10=2/5

• ❷To convert a percent to decimal ,we drop the per cent sign and shift the decimal point by two places to the left.Ex:32%=32/100=0.32

• ❸To convert a ratio into a percent we write as a fraction , then multiply the symbol[%] after the product .Ex:12:25=12/25 (12/25x100)%=48%

❹To convert a fraction to a percent, we multiply the fraction by 100 and put the

symbol %after the product.Ex:14/25 (14/25x100)=56%

❺ To convert a decimal to percent we multiply by 100 and insert (%) sign or to convert a decimal into a percent, we shift

the decimal point to the right and insert % sign.Ex:0.25=(0.25x100)%=25%

Tips❶10% of 543

10%x54354.3

❷50%of444divide by 2

222❸5%of44Divide by 2

44/2

22Take 10%

22x10=2.2❹15% of 24

Break them into 2 parts10%+5%

10%x24=2.45of24

24/2=12take 10%=1.2

12+1.23.6

❺95% Of Rs2400Break 95% into 2 parts

100%-5%100of2400

24005%of2400

2400/21200

10%of 1200120.0

2400-120video

ApplicationsPercentages are used in calculating our marks in tests.Used in items behind the

cover[VAT[value added tax]].Shops advertise discounts.These dicounts are percentages.They are used in housing

loans or and any other loans.Companies describe their profit and loss in percentage.The country’s

population is described in percentage.

They are used in sales.They are used in showing the divisions of

water[Salty,sweet,iceglaciors,and fresh water].They are used in showing the usage of water in

different countries.

Illustration1

Sinu bought a set of books for Rs 400 and sold it for Rs380.Find his loss and the loss percent

Sol: S.P=Rs380 C.P=400RsS.P<C.PLoss=C.P-S.PLOSS=Rs20loss%=Loss /C.PX10020/400X100=5%

Illustration2

• Arvind earns Rs12,000 per month .He spends 30% of his monthly income on house rent, 40% on household expenses ,5% on travel ,and 5% on entertainment for his family .The remaining is saved in the bank .Find out how much does Arvind spend on each item and how much he saves.

Solution :Total income for the month =Rs12,000House rent :30% of Rs12,000

12000x30/100=Rs3,600Household expenses=40% of Rs12000

12000x40/100=Rs4,800Travel expenses=5%of Rs 12000

12000x5/100=Rs600Entertainment =5%of Rs12000

12000x5/100=Rs600Total expenses=30%+40+5%=5%=80%

Savings=Income-Expenditure 100-80=20%

Actual Savings =12000X20/100=Rs3,400

Conclusion

• At last we would like to conclude that percentages are very important in human life and the topic profit and loss is also very important.So, we think that you all understood about the topic percentage and its applications

Thank

You

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