Profit and Loss Answer it!

A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180 . After one more such change the price is further reduced by $153 Find the original price of the article. GIve proper explanation

Thanks in advance

let x = X/100, and let the original price = P

P - P(1+x)(1-x) = 180
P(1- 1+x^2) = 180
P= 180/x^2 ................... [ I ]

(P-180) - (P-180)(1-x^2) = 153
(P-180) = 153/x^2 ........ [ II ]

[ I ] / [ II ]
P/(P-180) = 180/153
153P = 180(P-180)
27P = 180*180
P = $1200
----------------

1.) 153/180 = 0.85
1-0.85 = 0.15 or 15%

2.) 180/15= 12
12 x 100 = 1200

3.)1200/115 = 10.43478260869565
10.43478260869565 x 100 = 1043.478260869565

Step 1 works out how much what percentage x refers to by examining the decrease between 180 and 153

Step 2 works out how much the product cost before it began to decrease in value by using the decrease of 180 and working out the percentage it refers to

Step 3 works out what the original value of the product was by reducing it by the percentage x which we now know to be 15%

=$1043.48c