Every day we purchase one thing or the other, and every product has a certain price. So, the price that we pay to the seller to buy the product is called the “selling price,” whereas the amount at which the product is bought by the seller is known as the “cost price.”
Based on the cost price and selling price of a product a profit and loss are determined. If a person buys a product at one price and sells it at a different price, then he makes a profit or loss on that product. If the selling price of an item is greater than the cost price, then the seller gains a profit. If the selling price of an item is less than its cost price, the seller faces a loss.
What is Selling Price?
Selling price is the amount a customer pays for a product or service. It includes the value of the offering and the cost of selling it.
The price at which a product or commodity is sold by a merchant to a consumer is known as the “selling price”. Sales of a product are based on the selling price of the product. The amount that is paid by a buyer to buy a product is called the “actual selling price”. If the consumer buys a product at a price higher than the product’s cost, the merchant will gain a certain profit, and if a product is sold at a lower price than its cost price, a loss is incurred in the transaction. Therefore, the selling price of the product is:
SP = CP + P
SP = CP – L
where,
- Selling Price (SP): Selling price is the amount paid by the customer to buy a product.
- Cost price (CP): Cost price is the amount paid by a merchant or retailer to buy a product or commodity.
- Profit (P): Amount gained by selling a product or commodity at a price that is higher than its cost price is called “profit”.
Also,
Loss (L): The amount that is incurred by the seller after selling a product at a price that is less than its cost price is called “loss”.
- Loss formula = Cost price – Selling price (SP < CP)
Now, the formula for selling price in terms of profit percentage and loss percentage is:
SP = {(100 + P%)/100} × CP
SP = {(100 – L%)/100} × CP
Difference Between Selling Price and Cost Price
Cost price is the price paid by the merchant to acquire certain goods. The cost price is the minimum price at which any merchant can sell its product without incurring a loss, whereas the selling price is the price that a user pays for an article. The selling price is always less than or equal to the marked price.
Cost Price
The price at which the merchant acquires the product including the shipping cost is termed the Cost price. Profit and loss are calculated on the cost price. Generally, any merchant tries to sell its product at price greater than the cost price.
Marked Price (MP) and Discount
The price that is written on a product’s label by the merchant is called the “marked price.” A discount is always offered on a product’s marked price. Merchants or retailers offer discounts to consumers to attract them and increase the sales of a product.
- Discount = Marked price (MP) – Selling Price (SP)
- Discount Percentage = (Discount/MP) × 100
Now, the formula for selling price in terms of discount and the marked price is:
Selling Price = Marked Price (MP) – Discount
- Selling Price = Cost Price + Profit
- Selling Price = Marked Price – Discount
- Selling Price = (100+Profit)/100 × Cost Price
- Selling Price = (100−Loss)/100 × Cost Price
Question 1: At what price should the shopkeeper sell the goods to make a profit of 15% if the cost price of the product is ₨ 250.
Solution:
Given,
- Cost price of good = ₨ 250
- Profit percentage = 15%
Profit percentage = (Profit/Cost price) × 100
⇒ 15 = (Profit/ 250) × 100
⇒ Profit = ₨ 37.5
Profit = Selling price – Cost price
⇒ 37.5 = SP – 250
⇒ Selling price = ₨ 287.5
Therefore, selling price of good = ₨ 287.5
Question 2: A shopkeeper bought 200 pens at a cost of ₨ 1000. At what price should he sell each pen to gain a profit of ₨ 200.
Solution:
Given,
- Cost price of 200 pens = ₨ 1000
- Profit = ₨ 200
Profit = Selling price – Cost price
⇒ 200 = S.P – 1000
⇒ SP = 1200
⇒ Selling price of 200 pens = ₨ 1200
Now, selling price of one pen = 1200/200 = 6
Therefore, shopkeeper should sell one pen at ₨ 6 to gain a profit of ₨ 200.
Question 3: Samar buys a cycle at ₨ 2400 and sells it at a loss of 25%. What is the selling price of the cycle?
Solution:
Given,
- Cost price of the fan (C.P) = ₨ 2400
- Loss percentage is 25%
Loss percentage = (Loss/Cost price) × 100
Hence, Loss = ₨ 600
Loss = Cost price – Selling Price
600 = 2400 – S.P
⇒ Selling price = ₨ 1800
Hence, selling price of the cycle is ₨ 1800/-
Question 4: Anita bought 5 notebooks for ₨ 200. She sold them to her friend Sameera at a loss of ₨ 50. At what price did Sameera buy books from Anita.
Solution:
Given,
- Cost price of 5 note books = ₨ 200
- Loss = ₨ 50
Cost price at which Sameera bought books = the price at which Anita sold books.
Loss = Cost price – Selling price
⇒ 50 = 200 – S.P
⇒ Selling price = ₨ 150
Hence, price at which Sameera bought books = ₨ 150/-
Question 5: Vijay sold two umbrellas at a cost of ₨ 280. He sold one umbrella at a profit of 12% and the other umbrella at a loss of 5%. If the cost price of both umbrellas is the same, then what is the selling price of each umbrella?
Solution:
Given,
- Selling of two umbrellas = ₨ 280
- 1st umbrella is sold at a profit of 12%
- 2nd umbrella is sold at loss of 5%
Let the Selling price (S.P) of 1st umbrella = x
Selling price of 2nd umbrella = 280 – x
Cost price (C.P) = {100/(100 + Profit%)} × Selling price
⇒ C.P of 1st umbrella = {100/(100 + 12)} × x = (100/112) x
Cost price (C.P) = {100/(100 – Loss%)} × Selling price
⇒ C.P of 2nd umbrella = {(100/(100 – 5)} × (280 – x) = {100 × (280 – x)/95}
According to given data,
C.P of 1st umbrella = C.P of 2nd umbrella
⇒ (100/112) x = {100 × (280 – x)/95}
⇒ 95x = 112 × (280 – x)
95x = 31360 – 112x
⇒ 112x + 95x + 31360 ⇒ 207x = 31360
⇒ x = 151.5
⇒ S.P of 1st box = ₨ 151.5
⇒ S.P of 2nd box = 280 – 151.5 = ₨ 128.5
Hence, selling price of 1st umbrella = ₨ 151.50/- and the selling price of 2nd umbrella = ₨ 128.50/-
Question 6: The marked price of a fan is ₨ 1200. What is the selling price of the fan after a 10% discount.
Solution:
Given,
- Marked price of fan (M.P) = ₨ 1200
- Discount percentage = 10%
Discount percentage = (Discount/Marked price) × 100
⇒ 10 = (discount/1200) × 100
⇒ Discount = ₨ 120
Discount = Marked price – Selling Price
⇒ 120 = 1200 – S.P
⇒ S.P = ₨ 1080
Hence, selling price of the fan is ₨ 1080/-
Question 7: A shopkeeper sold a bag at ₨ 300 and gained a profit of 15%. At what price should he sell the bag such that he faces a loss of 15%?
Solution:
Given,
- Selling price of bag = ₨ 300
- Profit percentage = 15%
Cost price (C.P) = {100/(100 + Profit%)} × Selling price
⇒ C.P = {100/(100 + 10)} × 300
⇒ C.P = ₨ 260.87
Loss percentage = 15%
Loss percentage = (Loss/Cost price) × 100
⇒ 15 = (Loss/260.87) × 100
⇒ Loss = ₨ 39.13
Loss = Cost price – Selling price
⇒ 39.13 = 260.87 – S.P
⇒ S.P = ₨ 221.84
Hence, to face a loss of 15% the shopkeeper must sell the bag at ₨ 221.84/-
Q1: A shopkeeper buys a bicycle for Rs. 2500 and sells it at a profit of 20%. Calculate the selling price of the bicycle.
Q2: A mobile phone originally priced at Rs. 15,000 is sold at a discount of 10%. Find the selling price of the mobile phone after the discount.
Q3: A laptop is sold for Rs. 40,000 at a profit of 25%. What was the cost price of the laptop?
Q4: A pair of shoes is sold for Rs. 1800, resulting in a loss of 10%. Find the cost price of the shoes.
Q5: A watch is sold at Rs. 900, making a profit of 20%. Find the cost price of the watch.
Find the formula of the selling price when the profit percent is given.
Formula of the selling price when profit percent is given
SP = {(100 + P%)/100} × CP
What is the difference between the marked price and the selling price?
Marked Price is the price that is printed on the product, whereas selling price is the price that is paid by the consumer after all discounts and negotiations.
What is the formula for Cost Price and Selling Price?
Formula for CP and SP are,
What is profit?
When selling price is greater than the cost price, then the difference in the selling price and cost price is termed profit.
What is the selling price formula with a discount?
When a discount is given on the marked price of any object then the selling price is calculated as
Selling Price = Marked Price – Discount
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