Percent is derived from a phrase in latin “per centum” which means per hundred. It is a ratio with base (denominator) 100. It evolved as a concept so that there can be a uniform platform for comparing different values.
To express x% as a fraction, divide it by 100 ⇒ x% = x/100
To express a fraction as %, multiply it by 100 ⇒ x/y = [(x/y) × 100] %
x% of y is given by (y × x/100 )
1/4 = 25%
1/5 = 20%
1 /6= 16.66%
1/7 = 14.28%
1/8 = 12.5%
1/9 = 11.11%
1/10 = 10%
1/11 = 9.09%
1/12 = 8.33%
Shortcuts
If X’s income is a% more than Y’s income, the Y’s income is less than X’s income by
[ a / (100+a)] * 100%
If ‘M’ is x% of ‘N’ and ‘P’ is y% of ‘N’ then
‘M’ is (x/y) * 100% of ‘P’.
If the sides of the triangle, rectangle, square, circle, rhombus etc is
(i) Increased by a%. Its area is increased by
2a+(a2/100)
(ii)If decreased b%. Its areas is decreased by,
-2b+(b2/100)
The population of a town is ‘P’. It increased by x% during 1st year, increased by y% during 2nd year and again increased by z% during 3rd year. The population after 3 years will be,
P *[(100+x)/100] * [(100+y)/100] * [(100+z)/100]
