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:
| Thus, 20% = |
20 |
= |
1 |
. |
| 100 |
5 |
To express : a/b as a percent;
|
|
We have, |
a |
= |
 |
a |
x 100 |
 %. |
|
b |
b |
| Thus, |
1 |
= |
|
1 |
x 100 |
% |
= 25%. |
| 4 |
4 |
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 |
x 100 |
 % |
| (100 + R) |
If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:
|
R |
x 100 |
% |
| (100 - R) |
Results on Population:
Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
| 1. Population after n years = P |
|
1 + |
R |
|
n |
| 100 |
| 2. Population n years ago = |
P |
|
1 + |
R |
|
n |
| 100 |
|
Results 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 |
|
n |
| 100 |
2. Value of the machine n years ago :
|
P |
|
1 - |
R |
|
n |
| 100 |
|
3. If A is R% more than B, then B is less than A by:
|
|
R |
x 100 |
%. |
| (100 + R) |
4. If A is R% less than B, then B is more than A by:
|
|
R |
x 100 |
%. |
| (100 - R) |