# Percentages

Concept of Percentage:

·                      x% as a fraction:  x% = x/100

·                     To express  a/b as a percent: 100a/b %

·                     If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the

expenditure is     100 R %/(100+R)

·                     If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is 100 R %/(100-R)

·                     Percentage increased / decreased is given by = (ending value-intial value) x 100/intial value

If answer is +ve then value is  increased.

If answer is –ve then value is decreased.

Results on Population:

·                     Population after n years =  P(1 + R/100)n,where R is the rate increase. R will be negative if population is decreased.

·                     Population n years ago = P/(1 + R/100)n.

Results on Depreciation:

·                     Value of the machine after n years  = P(1 - R/100)n, where R is the rate of depreciation.

·                     Value of the machine n years ago =  P/ (1 - R/100)n.

·                     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

Conversions (Important):

·100 % =1                     150% = 3/2                          60% = 3/5            33.33 % = 1/3                     66.67% =   2/3

125% = 5/4                    50% = 1/2     40 % = 2/5    80 % = 4/5    75 % = 3/4

20% = 1/5                               120 % = 6/5                          25% =  1/4                             16.66% =  1/6                       110%= 11/10

12.5%= 1/8                6.25 % = 1/16           11.11 % = 1/9            10% = 1/10