### PERCENTAGES-

The word “Percent” indicates “for every hundred”. This idea is developed to facilitate easier evaluation of fractions by equalizing the denominator to hundred.**Example: - **

7/11 as a percentage is represented as

__Percentages can also be represented as decimal fractions. In such a case, it is effectively equivalent to proportion of the original quantity.__

**Example**

20% is the same as = 20/100 i.e., 0.2.

Any percentage can be stated as a decimal fraction by dividing the percentage figure by 100.

If the ratio of A & B is 3:2, we can say the ratio of A: B is 60%:40%.

Expressing x% as a fraction:-

X%= x out of 100=(x/100)

So, 75% = 75 out of 100 = (75/100) = (3/4)

Any percentage can be expressed as a decimal fraction by dividing the percentage figure by 100.

0.5 = (0.5 x100)/100 = (50/100) =50%

0.25= (0.25 x100)/100 = (25/100) =25%

0.2= (0.2 x 100)/100= (20/100) = 20%

X as a percent of Y = (X/Y) x 100

Y as a percent of X = (Y/X) x 100

Percentage Increase or Decrease:-

Percentage increase or decrease of a quantity is the ratio expressed in percentage of the actual increase or decrease of the quantity & the original amount of the quantity i.e.

Percentage Increase

If the production of rice went up from 225MT in 1993 to 242MT in 1994, then the percentage increase in rice production from1993 to 1994 is calculated as follows:

Actual Increase= 242-225=17 MT

Here this increase of 17MT is on 225 MT. (which is considered as the base for calculating the percentage increase).

Percentage Increase

Whenever there is any percentage increase or decrease on a quantity, the new value of the quantity can be calculated directly, instead of actually calculating the increase / decrease on the original quantity & then adding to/ subtracting from the original quantity.

If the increase on a figure of 350 is 15%, the new quantity is 1.15 x 350 = 402.5 (where 1.15 = 1+ 0.15, 0.15 being the decimal equivalent of 15%).

Similarly, if there is a decrease of 12% on a quantity of 225, then the new quantity will be equal to 225 x 0.88 = 198( where 0.88 = 1-0.12, 0.12 being the decimal equivalent of 12%).

2) 3

Any percentage can be stated as a decimal fraction by dividing the percentage figure by 100.

__Ratio b/w any two quantities can also be expressed as a percentage__.

**Example**

If the ratio of A & B is 3:2, we can say the ratio of A: B is 60%:40%.Expressing x% as a fraction:-

X%= x out of 100=(x/100)

So, 75% = 75 out of 100 = (75/100) = (3/4)

Any percentage can be expressed as a decimal fraction by dividing the percentage figure by 100.

### Expressing decimal as a percentage:-

__Any decimal fraction can be converted into percentage by multiplying it by 100.__0.5 = (0.5 x100)/100 = (50/100) =50%

0.25= (0.25 x100)/100 = (25/100) =25%

0.2= (0.2 x 100)/100= (20/100) = 20%

**Note:-**

**1)**When two numbers X & Y are given, then one number can be expressed as a percentage as a percentage of the other, in the following way.

X as a percent of Y = (X/Y) x 100

Y as a percent of X = (Y/X) x 100

**2)**X% of Y = Y% of X

Percentage Increase or Decrease:-

Percentage increase or decrease of a quantity is the ratio expressed in percentage of the actual increase or decrease of the quantity & the original amount of the quantity i.e.

Percentage Increase

Percentage decrease

**Example**

If the production of rice went up from 225MT in 1993 to 242MT in 1994, then the percentage increase in rice production from1993 to 1994 is calculated as follows:Actual Increase= 242-225=17 MT

Here this increase of 17MT is on 225 MT. (which is considered as the base for calculating the percentage increase).

Percentage Increase

**Note: -**For calculating the percentage increase or decrease, the base is always the original quantity.

Whenever there is any percentage increase or decrease on a quantity, the new value of the quantity can be calculated directly, instead of actually calculating the increase / decrease on the original quantity & then adding to/ subtracting from the original quantity.

**Example**

If the increase on a figure of 350 is 15%, the new quantity is 1.15 x 350 = 402.5 (where 1.15 = 1+ 0.15, 0.15 being the decimal equivalent of 15%).Similarly, if there is a decrease of 12% on a quantity of 225, then the new quantity will be equal to 225 x 0.88 = 198( where 0.88 = 1-0.12, 0.12 being the decimal equivalent of 12%).

**Examples:**

**1)**The prices of rice at a shop in the months of July & August were ₹30 per kg & ₹ 36 per kg respectively. What is the percentage increase in the price of rice from July to August?

**2)**In an examination having 120 questions, Akhil answered 45% of the first 60 questions correctly & 75% of the next 60 questions correctly. What percentage of questions in the examination did he answer correctly?

**Solution:-**Number of questions Akhil answered correctly in first 60 questions

Number of questions he answered correctly in the next 60 questions

Percentage of questions he answered correctly

### Exercise Problems:-

**1)**Akhil donates 15% of his monthly income every month which is ₹ 1875. What is his annual income?

**2)**Raju spent ₹ 12024 to buy a washing machine, ₹ 8016 to buy a television & saved the rest amount of 25%. What was the total amount with raju?

**Solutions:-**1) 3

2) 3

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