MATHS QUERY
Profit, Loss and Discount
Introduction
We do shop for our daily use products or grocery items for home use or as smallest as an attractive wrist watch. The price written on the tag of watch is a marked price.
Customers buys the watch for a price paid to shopkeeper, that price is a selling price of watch.
The shopkeeper must have bought that watch from its manufacturer for a price, that price paid by
shopkeeper to manufacturer is a cost price of watch.
There arises three cases depending upon at what price shopkeeper sells the watch.
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Case 1: Watch sold at price more than its cost price
When shopkeeper sells the watch at price more than the price he paid when he bought it from manufacturer, then he earns extra money. The extra money he earned is a profit to shopkeeper.
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Case 2: Watch sold at price less than its cost price
When shopkeeper sells the watch at price less than the price he bought it for his shop, then he does not earn any money even equal to its cost price. In this case, shopkeeper is in loss.
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Case 3: Watch sold at price equal to its cost price
When shopkeeper sells the watch at same price as its cost price, then the shopkeeper does not earn and lose any money. This is the case of no profit and no loss.
Let’s next dive into more details of profit, loss and discount and see how they are calculated in numbers with their formulas.
Cost price
The amount of money paid to buy a product is called cost price of the product.
A shopkeeper buys a product from a manufacturer or a wholesaler. The amount paid by the shopkeeper to buy
the product is cost price of the product.
It is written as C.P.
A shopkeeper bought a watch to sell on his shop to customers from the manufacturer. He paid $50 to manufacturer. So, $50 is the cost price of watch for the shopkeeper.
Selling price
The amount of money at which a product is sold for is called selling price of the product.
When a shopkeeper sells a product to customer and the price at which he sells it
is selling price of the product.
It is written as S.P.
The shopkeeper sells the watch at $70 to customers. So, $70 is the selling price of watch.
Profit
When selling price of a product is more than its cost price, then the extra amount of money earned is called
profit.
When shopkeeper sells product at more than its cost price, then he earna extra amount of money, which is
a profit to the shopkeeper.
Profit is calculated as difference between the selling price and cost price of a product.
Profit = SP – CP
If SP and profit are given, then CP is calculated as
CP = SP – ProfitIf CP and profit are given, then CP is calculated as
SP = CP + Profit
The Shopkeeper bought the watch at cost price of $50 and sells it at selling price of $70.
So, the profit made by shopkeeper can be calculated as
Here, SP = $70 and CP = $50
\(\because\) Profit = SP – CP
\(\therefore\) Profit = 70 – 50 = 20, which is $20, a profit.
Loss
When selling price of a product is less than its cost price, then the amount of money lost is called
loss.
When shopkeeper buys product at more than its selling price, then he does not earn any extra amount of money
rather lose money and suffers loss.
Loss is calculated as difference between the cost price and selling price.
Loss = CP – SP
If CP and loss are given, then SP is calculated as
SP = CP – LossIf SP and loss are given, then CP is calculated as
CP = SP + Loss
Let’s take another example, where shopkeeper suffers loss.
Let’s say shopkeeper sold the watch with selling price of $40, which is lesser than its cost
price of $50.
So, the loss made by shopkeeper can be calculated as
Here, SP = $40 and CP = $50
\(\because\) Loss = CP – SP
\(\therefore\) Loss = 50 – 40 = 10, which is a $10, a loss.
Overhead charges
Overhead charges are those additional charges in terms of amount of money that is paid for products before selling it. It can include labour charges, maintenance charges, freight charges or any type of taxes paid on products etc.
When a shopkeeper buys products from the manufacturer premises, he has to pay freight charges to transport the products to his place. The additional amount of money paid as freight charges is an example of overhead charges.
The shopkeeper in our example, if pays an $5 as freight charges to transfer the packet from manufacturer to his shop, then $5 is counted as overhead charges paid by the shopkeeper.
Effective cost price
Effective cost price includes cost price of a product and the overhead charges paid for the product.
Effective cost price = cost price + overhead charges
Again, the shopkeeper paid $5 as overhead charges to transfer the watch
from manufacturer to his shop and the cost price of watch is $50.
Cost price = $50
Overhead charges = $5
\(\because\) Effective cost price = cost price + overhead charges
\(\therefore\) Effective cost price = 50 + 5 = 55, which is $55, as effective cost price.
Profit percentage
Profit percentage is the amount of profit earned out of one hundred amount of cost price.
\(Profit \% = \frac{Profit}{CP} \times 100\)
The shopkeeper sells the watch with selling price of $70, whose cost price is $50.
Cost price = $50
Selling price = $70
\(\because\) Profit = SP – CP
\(\therefore\) Profit = 70 – 50 = 20
Also, \(Profit \% = \frac{Profit}{CP} \times 100\)
\(\therefore\) \(Profit \% = \frac{20}{50} \times 100\) = 40, which is 40% profit.
Loss percentage
Loss percentage is the amount of loss out of one hundred amount of cost price.
\(Loss \% = \frac{Loss}{CP} \times 100\)
When the shopkeeper sells the watch with loss with selling price of $40, whose cost price is $50.
Cost price = $50
Selling price = $40
\(\because\) Loss = CP – SP
\(\therefore\) Loss = 50 – 40 = 10
Also, \(Loss \% = \frac{Loss}{CP} \times 100\)
\(\therefore\) \(Loss \% = \frac{10}{50} \times 100\) = 20, which is 20% loss.
Marked price
Price that is written on sale tag of a product is called as marked price.
It is also called as list price or print price.
Discount
Discount is the amount deducted from the marked price to reduce its selling price.
It is written as MP.
When the shopkeeper sells a product at less than its marked price, the amount of deducted price is the
discount on the product.
Discount = MP – SP
If, the marked price of watch is $100 and the selling price is $70.
So, Marked price = $100
Selling price = $70
\(\because\) Discount = MP – SP
\(\therefore\) Discount = 100 – 70 = 30, which $30 discount.
Discount percentage
Discount percentage is the amount of discount on a product out of one hundred amount of marked price.
\(Discount \% = \frac{Discount}{MP} \times 100\)
The shopkeeper sells the watch at selling price of $70, whereas marked price on packet is $100.
Selling price = $70
Marked price = $100
\(\because\) Discount = MP – SP
\(\therefore\) Discount = 100 – 70 = 30
Also, \(Discount \% = \frac{Discount}{MP} \times 100\)
\(\therefore\) \(Discount \% = \frac{30}{100} \times 100\) = 30, which is 30% discount percentage.