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.
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.