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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