Question

the price of coffee has been reduced by 8% by how much percent must the new prices increased to retain the original price

Answer 1

Let the original price be 100

Price after reducing = 100 - 100*8/100

= 92

So new price. = 92

Let increased percent be x

92+92*x/100 = 100

92*x/100= 100 - 92

92* X = 8*100

X= 800÷92 =8.69%

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The required percent is 8.69 percent.}}}$

Step-by-step explanation:

Let the original price of the coffee be x.

Then, after reducing the price by 8%, the reduced price of the coffee will be

$P_r=x-8\%\times x=x-\dfrac{8}{10}}x=x-\dfrac{2}{25}x=\dfrac{23}{25}x.$

Now, let y% be  increased to retain the original price.

Then, we must have

$P_r+y\%\times P_r=x\\\\\\\Rightarrow \dfrac{23}{25}x+\dfrac{y}{100}\times\dfrac{23}{25}x=x\\\\\\\Rightarrow \dfrac{23}{25}+\dfrac{y}{100}\times\dfrac{23}{25}=1\\\\\\\Rightarrow 1+\dfrac{y}{100}=\dfrac{25}{23}\\\\\\\Rightarrow \dfrac{y}{100}=\dfrac{2}{23}\\\\\Rightarrow y=\dfrac{200}{23}\\\\\Rightarrow y=8.69.$

Thus, the required percent by which the new price should be increased is 8.69%.

#Learn more

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Link : https://brainly.in/question/6148998.