DEFINITIONS AND FORMULAS
>Cost price (CP): The price at which a person buys a product. This cost price is further classified into two different categories:
Fixed Cost: The fixed cost is constant, it doesn’t vary under any circumstances
Variable Cost: It could vary depending on the number of units
>Selling/Sales price (SP): The price at which a person sells a product.
>Profit or Gain: When a person sells a product at a price greater than its cost price, a profit is earned. That is, if SP > CP, then the difference between them is called profit.
Profit/Gain = SP (Selling Price) – CP (Cost Price)
>Loss: When a person sells a product at a price lesser than its cost price, a loss is incurred. That is, if SP < CP, then the difference between them is called loss.
Loss = Cost price (CP) – Selling Price (SP)
>Profit or Loss Questions are always calculated on the cost price.
>Marked price: Marked price, also known as the listed price is the price marked as the selling price of the product. This is labeled by shopkeepers to offer a discount to the customers in such a way that,
Discount = Marked Price – Selling Price
And Discount Percentage = (Discount/Marked price) x 100
>Discount or Rebate: The discount on the product is calculated on the marked price.
These are a few of the basic formulas used in solving questions on profit and loss:
>Gain % = (Gain / CP) * 100
>Loss % = (Loss / CP) * 100
>SP = [(100 + Gain%) / 100] * CP
>SP = [(100 – Loss %) / 100]*CP
The above two formulas can also be written as,
If a product is sold at a gain of 10%, then SP = 110% of CP.
If a product is sold at a loss of 10%, then SP = 90% of CP.
>CP = [100 / (100 + Gain%)] * SP
>CP = [100 / (100 – Loss%)] * SP
Few Tricks
>For false weight, profit percentage will be P% = (True weight – false weight/ false weight) x 100.
>When there are two successful profits say m% and n%, then the net percentage profit equals to (m+n+mn)/100
>When the profit is m% and loss is n%, then the net % profit or loss will be: (m-n-mn)/100
>If P% and L% are equal i.e. if the percentage of profit and loss is equal, then P = L and there will always be a loss, %loss = P2/100.
>if Selling price of ‘x’ items=cost price of ‘y’ items, then profit/loss= (y-x)/x
Practice Problems:
1. A shopkeeper marks up his goods by 30% and then gives a discount of 30%. What is his percentage of profit or loss?
Solution: Let the cost price of the item be TK. 100. Then the marked price of the item is TK. 130. So, at a discount of 30%, the selling price of the item is TK. 91. Therefore, the percentage of loss is 9 %.
2. Rahul sold a painting for Taka 360 and made a 20% loss. What would be his selling price be if he were to sell the painting at 30% profit?
Solution: Let, cost price of the painting = X. So, at 20% loss, the selling price = 0.8X
According to question, 0.8X = 360. Or, X = (360 ÷ 0.8) = 450. So, at 30% profit, Selling Price = (450 x 1.30) = 585 tk
3. A shopkeeper buys a dozen eggs at TK. 96. What should be the selling price of each egg if he wants to make a profit of 10%?
Solution: The cost price of each egg = 96/12 = 8 . So the selling price each egg = 8*1.1 = 8.8
4. The selling price of 10 pens is equal to the cost price of 6 pens. What is the percentage of profit or loss here?
Solution: Let, the cost price of 1 pen=Tk.1
so, cost price of 6 pens=Tk. 6---------→ this is the selling price of 10 pens (According to the question)
so, cost price of 10 pens=Tk. 10 & selling price of 10 pens=Tk.6
so a loss took place
loss=Tk. (10-6)=Tk. 4
so, percentage of loss= (4/10)*100=40%
5. By selling 100 pens, the gain is equal to the selling price of 20 pens. Percentage of gain?
Solution: A/Q,
Gain=SP of 100 pens - CP of 100 pens
i.e. SP of 20 pens=SP of 100 pens - CP of 100 pens
or, SP of 80 pens=CP of 100 pens
As per the formula, Gain {(100-80)/80} or 25%
6. If the discount is 30%, then the profit is 40%. What will be the profit if the discount is 40%
Solution: Let,
CP=TK. 100
SP= TK. 100*140%=100*(140/100)=Tk. 140
MP= Tk. 140/70%=(140*100)/70=Tk. 200
If the discount is 40%, then the SP will be Tk. 200*60%=tk. 120
so, percentage of profit={(120-100)/100}*100=20%
or,
MP= Tk. 100
SP= Tk. 100*70%=Tk. 70tf
CP= Tk. 70/140%=Tk. 50
if the discount is 40%, then new SP, SP'=Tk. 60
so, profit= Tk. (60-50)= Tk. 10
Percentage of profit, (10/50)*100=20%
7. A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Tk.55 more, he would have made a profit of 40%. What was the cost of the article in Tk?
Solution: Let,
Cp of the product is Tk. x
SP of the product is Tk. (x*90%) or Tk. 9x/10
if he had bought it for 20% less, then CP'=Tk. (x*80%) or Tk. 8x/10
if he had sold it for Tk. 55 more, then SP'=Tk (9x/10)+55
A/Q,
(9x/10)+55=140%*(8x/10)
or, (9x+550)/10=112x/100
or, 90x+5500=112x
or, x=Tk. 250
so, the cost price of the product was Tk. 250
8. A salesman makes 45% profit on every set of TV he sells. During a sale, he reduces his margin of profit to 40% while his sales increase by 10%. What is the ratio of his new total profit to the original profit?
Solution: Let,
Cost Price of one TV is Tk. 100
Selling Price is Tk. 145 (45% profit)
Initial sold quantity 100
Profit earned=Tk. {(145-100)*100}=Tk. 4500
Again,
New selling price is Tk. 140 (reduced margin of profit to 40%)
New Sold quantity 110 (sales increased by 10%)
Profit earned=Tk. {(140-100)*110}=Tk. 4400
so, the ratio of his new total profit to his original profit is 4400:4500 or 44:45
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