Published: 05 Aug 2019

**1. Concept of percentage :** Percent implies “for every hundred” and the sign % is read as percentage and x % is read as x per cent. In other words, a fraction with denominator 100 is called a per cent. For example, 20 % means 20/100 (i.e. 20 parts from 100). This can also be written as 0.2.

* To express x% as a fraction :* we have, x% = x/100.

Thus, 20% = 20/100 = 1/5;

48% = 48/100 = 12/25, etc.

* To express a/b as a percent :* we have, a/b = (a/b X 100)

Thus, 1/4 = (1/4 X 100)% = 25%;

0.6 = 6/10 = 3/5 = (3/5 X 100)% = 60%

**2.** If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is

**[R/(100+R) X 100%]**

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is

** [R/(100-R) X 100%]**

**3. Results on Population :** Let the population of a town be P now and suppose is increases at the rate of R% per annum, then :

1. Population after n years = **P(1 + R/100) ^{n}**

2. Population n years ago = **P/(1+ R/100) ^{n}**

**4. Result on Depreciation :** Let the present value of a machine be p. Suppose it depreciates at the rate of R% per annum. Then :

1. Value of the machine after n years = **P(1 - R/100) ^{n}**

2. Value of the machine after n years = **P/(1- R/100) ^{n}**

**5.** If A is R% more than B, then B is less than A by

** [R/(100 + R) X 100]%**

If A is R% less then B, then B is more than A by

**[R/(100 - R) X 100]%**

**Important Points to Note**

When any value increases by

10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)

20%, it becomes 1.2 times of itself.

36%, it becomes 1.36 times of itself.

4%, it becomes 1.04 times of itself.

Thus we can see the effects on the values due to various percentage increases.

When any value decreases by

10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)

20%, it becomes 0.8 times of itself

36%, it becomes 0.64 times of itself

4%, it becomes 0.96 times of itself.

Thus we can see the effects on a value due to various percentage decreases.

__Note:__

1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.

2. The percentage increase or decrease depends on the decimal multiplied.

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