Question

A number is increased by 15% and then it is decreased by 20% . Find the net increase or decrease percent

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Answer 1

Answer:

Number increases by 15%

100+15% of 100

100=15/100×100

100+15=115

There,

resulting the numbers decrease by its 20%

=115-(20% of 115)

=115‐(20/100×115)

115-20=95

Now,net increases =95-100= -5

Increases%=5/100×100

increases%= -5%

Answer 2

• Let the original number be x

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First it is increased by 15%

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$\sf :\implies \:{\bold{New \: number = x + \dfrac{15\times x}{100} }}$

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$\sf :\implies \:{\bold{New \: number = x + \dfrac{3\times x}{20} }}$

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$\sf :\implies \:{\bold{New \: number = x + \dfrac{3x}{20} }}$

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$\sf :\implies \:{\bold{New \: number = \dfrac{ 20x + 3x}{20} }}$

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$\sf :\implies \:{\bold{New \: number = \dfrac{23x}{20} }}$

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Now , the new number is decreased by 20%

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$\sf :\implies \:{\bold{New \: number = \dfrac{23x}{20} - \dfrac{20\times 23x}{100\times 20 } }}$

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$\sf :\implies \:{\bold{New \: number = \dfrac{ 23x}{20} - \dfrac{23x}{100} }}$

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$\sf :\implies \:{\bold{New \: number = \dfrac{23x\times 5 - 23x }{100} }}$

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$\sf :\implies \:{\bold{New \: number = \dfrac{115x - 23x}{100} }}$

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$\sf :\implies \:{\bold{New \: number = \dfrac{92x}{100} }}$

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$\sf :\implies \:{\bold{New \: number = \dfrac{46x}{50} }}$

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$\sf :\implies \:{\bold{New \: number = \dfrac{23x}{25} }}$

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• Comparing the original number and New number

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$\sf :\implies \:{\bold{Diff = x - \dfrac{23x}{25} }}$

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$\sf :\implies \:{\bold{Diff = \dfrac{25x - 23x}{25} }}$

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$\sf :\implies \:{\bold{Diff = \dfrac{2x}{25} }}$

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• Overall decreased percentage

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$\sf{\underline{\underline{\large{\bold{ Deceased\% = \dfrac{ decreased \: by}{Original \: number}\times 100 }}}}}$

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$\sf :\implies \:{\bold{ decreased\% = \dfrac{\dfrac{2x}{25}}{x}\times 100 }}$

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$\sf :\implies \:{\bold{ decreased\% = \dfrac{2x}{25}\div {x}\times 100 }}$

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$\sf :\implies \:{\bold{ decreased\% = \dfrac{2x}{25}\times\dfrac{1}{x}\times 100 }}$

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$\sf :\implies \:{\bold{ decreased\% = \dfrac{2}{25}\times 100 }}$

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$\sf :\implies \:{\bold{ decreased\% = \dfrac{2}{5}\times 20 }}$

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$\sf :\implies \:{\bold{ decreased\% = 2\times 4 }}$

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$\sf :\implies \:{\bold{ decreased\% = 8\%}}$

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• Therefore overall decreased % = 8%

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