The Basic Concept Of Percentage

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:

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?
\( {{10 \over 100+10} × 100} \)  \( = {{10 \over 110}×100} \) \(= 9 {1 \over 11}\% \)