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) × 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
