# Percentage Formulas, Shortcuts, Tips and Tricks

## Solved Examples on Percentage

Example: Find $26\frac{1}{2}$ % of 2000.

Solution. of 2,000 = $\frac{53}{2}\times \frac{1}{100}\times 2000$ = 530

Example: Two numbers are 25% and 40% more than a third number. What is the first number as a percentage of the second number ?

Solution. If the third number is 100 then the first two numbers are 125 and 140.
$\therefore$ The first number as a percentage of the second $\Rightarrow \frac{125}{140}\times 100\,=\,\frac{625}{7}\,=\,89\frac{2}{7}$ %

Example: Two number are 40% and 60% more than a third number. By what percentage is the first number less than the second number?

Solution. If the third number is 100 then the numbers are 140 and 160.
$\therefore$ first number is 20 less then the second number.
$\therefore$ Required percentage = $\frac{20}{160}\times 100$ = 12.5%

Example: 50% of 20% of a number is what percent of 50% of 5% of the same number ?

Solution: $\frac{50}{100}\times \frac{20}{100}\,=\,\frac{x}{100}\times \frac{50}{100}\times \frac{5}{100}$
$\therefore x\Rightarrow 400$

Example: Manoj gets 40% more than Suresh. How much percentage does Suresh get less than Manoj ?

Solution. Let Suresh’s salary be Rs 100.
$\therefore$ Manoj’s will be =100+40% of 100= Rs 140.
$\therefore$ Suresh gets Rs 40 less than Manoj’s salary.
$\therefore$ Required percentage = $\frac{40}{140}\times 100\,=\,28\frac{4}{7}$ %

Alternate method : The problem can be done by using the formula $\frac{100x}{100+x}\%\,=\,\frac{100\times 46}{140}\,=\,28\frac{4}{7} \%$

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