Profit, Loss and Discount

Profit, Loss and Discount

Profit, Loss and Discount Terminology

  • Cost Price (CP) : - The money paid by the shopkeeper to the manufacturer or whole saler to buy the goods is called cost price of the goods purchased by the shopkeeper.
    Note - If an article is purchased for some amount and there are some additional expenses on transportation, labour, commission etc., these are to be added in the cost price (CP). Such expenses are called overhead expenses.
  • Selling Price (SP) : - The price at which the shopkeeper sells the goods is called selling price (SP) of the goods sold by shopkeeper.
  • Profit : -If the selling price (SP) of the goods is more than its cost price (CP) price, then the dealer or shopkeeper makes a profit or gain.
    $$ Profit = SP - CP, \;\;SP > CP$$
  • Loss : - If the selling price (SP) of the goods is less than its cost price (CP),then the shopkeeper suffers a loss. $$Loss = CP - SP , \;\; CP>SP$$

Important Formula : -

  • $$Profit = SP - CP$$
  • $$Loss = CP - SP$$
  • $$Profit\;percentage=\frac{profit}{cost\;price}\times100$$
  • $$Loss\; percentage=\frac{loss}{cost\;price}\times100$$
  • $$SP=\left( \frac{100+gain\%}{100}\times CP\right)= \left(\frac{100-loss\%}{100}\times CP\right )$$
  • $$CP=\left( \frac{100}{100+gain\%}\times SP\right)= \left(\frac{100}{100-loss\%}\times SP\right )$$
  • $$SP=(100 + k)\%\;of\;CP;\; when \;profit=k\% \;of\; CP$$
  • $$SP=(100 - k)\%\;of\;CP;\; when \;loss=k\% \;of\; CP$$
    Note : - Profit or loss is always calculated on the basis of cost price unless otherwise metioned in the problem.

Mark up and Discount

  • Marked Price : - Basically to avoid loss due to bargaining by the customer and to get the profit over the cost price trader increases the cost price by a certain value, this increase in value over cost price is known as markup and the increased price (ie., CP + Markup) is called marked price or printed price or list price of the goods.
    $$Markup\;Price=CP + Markup$$ $$Marked\;Price = CP + (\% \;markup\; on\;CP)$$
    Generally goods are sold at marked price,if there is no further discount, then in this case selling price equals to marked price.
  • Discount : - Discount means reduction of marked price to sell at a lower rate or literally duscount means concession.basically it is caluculated on the basis of marked price.
  • $$\therefore \; Selling\;Price = Marked\;Price - Discount$$
  • $$or,\;\; Selling\;Price = Marked \;Price - (\%\;Discount\; on \;Marked\; Price)$$
  • $$Marked \;Price = CP + \% \;Markup\; on\; CP$$

Example 1. : -

  • If the cost price an artical is 200 and the percent markup is 30%.What is the marked price?
    Solution : -
    $$marked \;price = CP +\% \;markup\; on\; CP$$ $$=200+200 \times \frac{30}{100}$$ $$=260 \;Rs.$$

Example 2. : -

  • Find the cost price of an artical which is sold at Rs 110 at loss of 6 %.

Solution : -$$SP = Rs\; 110,\;Loss = 6\%.$$ $$then,\; SP = 94 \% \;of\; CP$$ $$110 = \frac{94}{100} \times CP $$ $$ CP =Rs\,117.02 $$

Profit, Loss and Discount Online Quizzes