A Person can gain profit only if Selling Price > Cost Price. Also, a person generates loss when Selling Price < Cost Price. So let’s understand each term in detail.
Selling Price (S.P)
Definition: The price at which a shopkeeper sells an item to a customer is known as the Selling price(S.P).
Formula: To calculate the selling price(S.P) when the (profit/cost) % is known:
Selling Price (S.P) = { [ ( 100 + Profit ) / 100 ] * C.P }
Selling Price (S.P) = { [ ( 100 – Loss) / 100 ] * C.P }
Cost Price (C.P)
Definition: The price at which a shopkeeper bought an item from a seller is known as the Cost price(C.P).
Formula: To calculate cost price(C.P) when the (profit/cost) % is known:
Cost Price (C.P) = { [ 100 / (100 + Gain ) ] * S.P }
Cost Price (C.P) = { [ 100 / (100 – Loss ) ] * S.P }
Profit
Definition: If the amount for which an item is sold is more than the amount at which that particular item is bought is called Profit.
Formula:
Profit = Selling Price(S.P) – Cost Price(C.P)
Loss
Definition: If the amount for which an item is sold is less than the amount at which that particular item is bought is called Loss.
Formula:
Loss = Cost Price(C.P) – Selling Price(S.P)
Profit Percentage
Formula:
Profit % = [ ( Profit * 100 ) / C.P ]
Loss Percentage
Formula:
Loss % = [ ( Loss * 100 ) / C.P ]
Selling Price(S.P) when Cost Price(C.P) & Gain % Or Loss % are given
Formula:
S.P when C.P and Gain % are given:
= [ (100 + Gain % ) / 100 * C.P ]
S.P when C.P and Loss% are given:
= [ (100 – Loss% ) / 100 * C.P ]
Cost Price(C.P) when Selling Price(S.P) & Gain % Or Loss % are given
Formula:
C.P when S.P and Gain % are given:
= [ 100 / ( 100 + Gain % )* S.P ]
C.P when S.P and Loss% are given:
= [ 100 / ( 100 – Loss % )* S.P ]
Examples
Example 1. A Student buys a book for ₹ 600 and sells it for ₹ 700. Find his gain and gain percent.
Solution:
Given, Cost Price of book = ₹ 600
Selling Price of book = ₹ 700
By using the gain formula,
Gain = Selling Price – Cost Price
= 700 – 600
= ₹ 100
By using the gain% formula,
Gain% = (gain/cost price) * 100
= (100/600) * 100
= 100/6
= 16.66%
Example 2. Sonia purchased a car for ₹ 450000. She used it for three months and then sold it for ₹ 435000. Find her loss percent?
Solution:
Given, C.P = ₹ 450000 and S.P = ₹ 435000
∴ Loss = C.P – S.P
= ₹ ( 450000 – 435000 )
= ₹ 15000
Loss % = [ ( Loss / C.P ) * 100 ] %
= [ ( 15000 / 450000 ) * 100 ] %
= 10/3 %
So, the loss percent = 10/3 %
Example 3. Sneha purchased a bicycle for ₹ 3500 and spent ₹ 1000 on its repair. She sold it at a gain of 40%. For how much did she sell the bicycle?
Solution:
Total cost price of the bicycle = price paid to purchase it + Repair charges
C.P = ₹ (3500 + 1000) = ₹ 4500
S.P = [ (100 + Gain % ) / 100 * C.P ]
= [ ( 100 + 40 ) /100 * ₹ 4500 ]
= ₹ 140/100 * 4500
= ₹ 6300
So, Sneha sold the bicycle for ₹ 6300
Example 4. A merchant lost 8% by selling an iPod for ₹12880. At what price should he sell if in order to gain 8%?
Solution:
S.P of the iPod = ₹12880 , Loss % = 8%
C.P of the iPod = [ 100 / ( 100 – Loss % ) * S.P ]
= [ ( 100 / 100 – 8 ) * ₹12880 ]
= ₹ 100 / 92 * 12880 = ₹ 14000
Now, C.P = ₹14000, Gain % = 8%
S.P of the iPod = [ (100 + Gain % ) / 100 * C.P ]
= [ ( 100 + 8 ) / 100 * ₹14000
= ₹ ( 108 / 100 ) * 14000
= ₹15120
So, he should sell the iPod at ₹15120 to gain a profit of 8%.
Example 5. A man bought goods worth ₹ 4500 and sold 1/3 of the goods at a loss of 10 %. At what gain percent should he sell the remaining goods so as to gain 20% on the whole transaction?
Solution:
C.P of goods = ₹ 4500, Gain = 20%
S.P of goods = [ (100 + Gain % ) / 100 * C.P ]
= [ ( 100 + 20 ) / 100 * ₹ 4500
= ₹ 120/100 * 4500
= ₹ 5400
C.P of 1/3 of the goods = ₹ (1/3 * 4500 ) = ₹ 1500
∴ S.P of 1/3 of the goods at a loss of 10%
= [ (100 – Loss% ) / 100 * C.P ]
= [ ( 100 – 10 ) /100 * ₹ 1500 ]
= ₹ 90/100 * 1500 = ₹ 1350
∴ S.P of the remaining goods = S.P of all the goods – S.P of 1/3 of the goods
= ₹ 5400 – ₹ 1350 = ₹ 4050
∴ C.P of the remaining goods = C.P of all the goods – C.P of 1/3 of the goods
= ₹ 4500 – ₹ 1500 = ₹ 3000
Gain = S.P – C.P
= ₹ 4050 – ₹ 3000 = ₹ 1050
Gain % = ( Gain /C.P ) * 100% = ( 1050/3000 ) * 100% = 35%
So, The man should sell the remaining goods at a gain of 35%.