In my earlier accounting article, I have mentioned about trade discount, cash discount, markup and down.
This article discussed the accountancy mathematic applied for trade discount:
Basics: (a) Trade Discount = List Price less Net Price (b) Amount of trade discount = List price x trade discount rate 
ILLUSTRATION 1 The list price of a pen is $200. A trade discount of 40% is offered. What is the net price of the belt? Solution: List price =$200
Trade discount = 40% x$200 = $80
Net price= List price less Trade discount = $200$80 = $120 

How to find Net Price? 
ILLUSTRATION 2
All shirts is given a 30% discount. What is the net price of a shirt that is listed at $400? Solution:
Trade discount=List priceNet price
Net price= List price â€“Trade discount
or alternatively
Net price(NP) =List price(LP) â€“Trade discount( r ) NP= LPLPr = LP(1r)
List price=$400 Trade discount =30% x $400 = $120
Net price =List priceTrade discount = $400 $120 =$280
ILLUSTRATION 3
The net price of a camera with a 30% trade discount is $500. What is the list price?
Solution:
Trade discount = List price â€“ Net price
Let the list price $X. Hence
Trade discount = 0.3X
$500 = X0.3X $500 = 0.7X X=$500/0.7 =$714.29 

More Complex Illustration: 
Shop A sells an item for $100 less 20% which Shop B sells the same item for $130 less 50%.
(a) Find the net prices of the items for the two shops? (b) What further discount % must be offered by the shop that sells at a higher net price in order to meet the competitor’s price?
Solution:
[ Net price(NP) =List price(LP) less Trade discount( r ) NP = LPLPr = LP(1r) ]
(a) Net price: Shop A=Net price =$100 (120%) =$80 Shop B=Net price =$130 (150%) =$65
(b) Shop A sells at a higher net price. Let the additional discount % be r% 65 = 80(1r) R= 35%
Therefore, Shop B should offer an additional 15% to meet Shop A’s price
