# Pecentage Calculation

We can use the following shortcuts for calculating percentages:

**Convert the percentage to fractions:**For example, if we want to find 12.5% of 124. We can solve this as given below â€“

**Use the following table for doing conversions of percentage to fraction:**

= 100% | = 50% | = 33.33% | = 25% | = 20% |

= 16.67% | = 14.28% | = 12.5% | = 11.11% | = 10% |

**Break the percentage into small parts:**Suppose you want to find 51% of 128. This can be found in a very easy way, as given below â€“**Interchange the number and percentage:**Suppose, we have to find 39% of 12.5. This will be equal to 12.5% of 39. So, we instead of finding 39% of 12.5, we can find 12.5 % of 39, which will be equal to 1/8*39 (as 12.5% is equal to 1/8).

For solving complex problems of percentages, we can use a mix of above three shortcut approaches.

# Some Important Conclusions

- if A is a% more than B then B is less than A by
- if A is a% less than B then B is more than A by
- if A number is increased by a% then decreased by a% then net change will be
- if a number is increased or decreased successively by a% and b% then net change is %
- if a number is first time increased by a% and then decreased by b% then net change is %
- if a number is increased successively by a%, b% and c% then net change is
- if in an examination a% of the student failed in one subject, b% failed in another subject and c% failed in both subject then the percentage of student who
- failed in either of subject = a + b - c
- passed in both subject = 100 - (a + b - c)

# 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:

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

# Results on Population

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

- Population after
*n*years = - Population
*n*years ago =

# Results on Depreciation

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

- Value of the machine after
*n*years = - 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