Question

a no. is increased by 8 % and then decreased by 10 % find net increase or decrease % _________ ​

Answer 1

Answer:

$let \: the \: number \: be \: x \\ according \: to \: question \\ when \: the \: number \: is \: increased \: by \: 8\% \\ then \: the \: number = x + x \times \frac{8}{100 } \\ = x + \frac{2x}{25 } \\ = \frac{25 x + 2x}{25} \\ \frac{27x}{25} \\ \\ when the \: number \: is \: decreased \: by \: 10\% \\ then \: the \: number \: = \frac{27x}{25} - \frac{27x}{25} \times \frac{10}{100} \\ \frac{27x}{25} - \frac{27x}{250} \\ = \frac{270x - 27x}{250} \\ \frac{243x}{250} \\ hence \: it \: is \: smaller \: than \: x \\ net \: decreasment = x - \frac{243x}{250} \\ \frac{250x - 243x}{250} \\ \frac{7x}{250} \\ net \: decrasement \: in \: \% = \frac{ \frac{7x}{250} }{x} \times 100\% \\ \frac{7x}{250} \times \frac{100}{x} \% \\ = 2.8\%$

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