The percentage concept has a major role in almost all the chapters of arithmetics.
So mastering this concept helps in solving questions of topics from sale, purchase, profit& loss, discount, interest, allegation and many more. Generally, the percentage is considered as per hundred or for every hundred.
The percentage is represented by the symbol
Some useful Formula in Percentage Concept
- When A is X
- When A is considered as X
- When two numbers are X
\begin{align*}\left( \dfrac {100+x}{100+y}\times 100\right) % \ of \ second \ number \end{align*} andÂ
    second number is
\begin{align*}\left( \dfrac {100+y}{100+x}\times 100\right) % \ of \ first \ number \end{align*}
similarly when the two numbers are X
\begin{align*}\left( \dfrac {100-x}{100-y}\times 100\right) % \ of \ second \ number \end{align*} andÂ
     second number is
\begin{align*} \left( \dfrac {100-y}{100-x}\times 100\right) % \ of \ first \ number \end{align*}
- If an amount is sucessively increased fist by X
- Let present population of a town is P and the population increases every year at a rate of r1, r2,r3,……rn up to n years thenÂ
population after n years is
\begin{align*}p\left( 1+\dfrac {r_{1}}{100}\right) \left( 1+\dfrac {r_{2}}{100}\right) \ldots \left( 1+\dfrac {r _{n}}{100}\right) \end{align*} put negative sign for decrease in population
when the population will increases at same rate r
- If a number A is successively increased by X
\begin{align*} A\left( 1+\dfrac {x}{100}\right) \left( 1+\dfrac {y}{100}\right) \left( 1+\dfrac {z}{100}\right) \end{align*}
- consider a product whose price increases by P