Question

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 1

Required value of k is 43% .

Step-by-step 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

`\text{{Sales price}} = x - 30(1)/(100)* x`

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

=>
`0.70x + (k)/(100)*0.70x = x`

=>
`0.70 + (0.70)/(100)k = 1`

=>
`(0.70)/(100)k=1-0.70`

=> 0.70k = 100 x 0.30

=>
`k = ((100*0.30))/(0.70)=42.857`that is 43

Hence required value of k is 43% .