A sports jacket is on sale for 30% off the regular price. After the sale, the same sports jacket is marked up k% to again sale at the original regular price. Kind k to the nearest whole number

Answer: Required value of k is 43% . Explanation:Lets assume original regular price of sports jacket = x On sale ,  price of jacket is reuced by 30%  Sales price = x - 30% 0f x [tex]\text{{Sales price}} = x - 30\frac{1}{100}\times x[/tex]Sales price= x – 0.30x Sales price= 0.70x Once sales is over price of jacket is increased by k%  That is Sales price + k% of Sales price = 0.70x +  k% 0.70x  Also given after increasing to k% , price becomes equal to regular price => 0.70x +  k% of 0.70x  = original regular price => [tex]0.70x + \frac{k}{100}\times0.70x = x[/tex]=>[tex]0.70 + \frac{0.70}{100}k = 1[/tex]=>[tex]\frac{0.70}{100}k=1-0.70[/tex]=> 0.70k = 100 x 0.30 =>[tex]k = \frac{(100\times0.30)}{0.70}=42.857[/tex]that is 43 Hence required value of k is 43% .