**1) Concept of Percentage:**

By a certain percent, we mean that many hundredths.

Thus, x percent means x hundredths, written as

**x%**.

To express x% as a fraction: We have,

**x% =x/100**

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

To express a/b as a percent: We have,

**(a/b)=((a/b)*100)%.**

Thus, 1/4 = ((1/4)*100)% = 25%.

**2. Percentage Increase/Decrease:**

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))*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))*100]%**

**3. Results on Population:**

Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

**i) Population after n years = P(1+(R/100))^n**

**ii) Population n years ago = (P)/(1+(R/100))^n**

**4. Results on Depreciation:**

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

i) Value of the machine after n years =

**P(1-(R/100))^n**

ii) Value of the machine n years ago =

**(P)/(1-(R/100))^n**

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

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

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

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

**Also read:**

Percentage Problems Shortcut and Tricks for Competitive Exams Free PDF Download

Percentage Problems Shortcut and Tricks for Competitive Exams Free PDF Download

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