The percentage can be divided into ‘per-cent-age’ which means ‘per every hundred’. It is denoted by the symbol %
Following calculations should be kept in mind:
| ( {1 over 1}= 100 % ) | ( {1 over 2} = 50 % ) | ( {1 over 3} = 33.33 % ) |
| ( {1 over 4} = 25 % ) | ( {1 over 5} = 20 % ) | ( {1 over 6} = 16.66 % ) |
| ( {1 over 7} =14.28 % ) | ( {1 over 8} = 12.5 % ) | ( {1 over 9} = 11.11 % ) |
| ( {1 over 10} =10 % ) | ( {1 over 11} = 9.09 % ) | ( {1 over 12} = 8.33 % ) |
And so on.
This can come in handy during certain calculations.
Comparison between two values of X and Y :
If we compare x to y then we assume y is always equal to 100%
When any question asked, what percent of x is y, then y will be written in the denominator.
Q. If x is 80% of y, what percent of x is y?
1st method :
( y = {100×100 over 80} x )
( y = 125% {of} x )
2nd method :
Let y is 100 then x = 80
(∴ Required % = {100 over 80}×100 = 125% )
Example1 – K is what % of N ?
[ {K over N}×100 = {K over N}% ]
If A is R % more than B then B is less than A by –
$$ {brack {R over 100+ R}×100}% $$
If A is R% less than B, then B is more than A by –
$$ {brack {R over 100-R}×100}% $$
Example. If Ram’s income is 10% more than that of Shyam’s income then, how much Percentage Shyam’s income is less than that of Ram’s income?
( {{10 over 100+10} × 100} )
(
= {{10 over 110}×100} ) (= 9 {1 over 11}% )