Maths Class: Profit and Loss Percentage

Basic Definitions and Formulas
Cost price (C.P.): This is the price at
which an article is purchased.
Selling price (S.P.): This is the price
at which an article is sold.
Profit or Gain: If the selling price is
more than the cost price, the
difference between them is the profit incurred.
Loss: If the selling price is less than
the cost price, the difference between them is the loss incurred.
Profit or Loss is always calculated on the cost price.
Marked price: This is the price
marked as the selling price on an
article, also known as the listed price.
Below is the list of some 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 be stated as,
If an article is sold at a gain of 10%,
then SP = 110% of CP.
If an article is sold at a loss of 10%, then SP = 90% of CP.
CP = [100 / (100 + Gain%)] * SP
CP = [100 / (100 – Loss%)] * SP
Profit and Loss: Solved Examples

Question 1: An article is purchased for #450 and sold for #500. Find the gain percent.
Solution:
Gain = SP – CP = 500 – 450 = 50.
Gain% = (50/450)*100 = 100/9 %

Question 2: A man sold a fan for #465. Find the cost price if he incurred a loss of 7%.
Solution:
CP = [100 / (100 – Loss %)] * SP
Therefore, the cost price of the fan = (100/93)*465 = #500

Question 3: A man bought some toys at the rate of 10 for #40 and sold them at 8 for #35. Find his gain or loss percent.
Solution:
Cost price of 10 toys = #40 → CP of 1
toy = #4.
Selling price of 8 toys = #35 → SP of 1 toy = #35/8
Therefore, Gain = 35/8 – 4 = 3/8.
Gain percent = (3/8)/4 * 100 = 9.375%

Profit and Loss Quiz: Practice Question
Formula: Profit or Gain = S.P. – C.P.
Formula: Loss = Cost price (C.P.) – Selling Price (S.P.)
If the loss incurred in a
transaction is 3/5th of the selling
price, find the loss percent.
A. 37
B. 37.5
C. 37.75
D. None
Anyone with the correct answer will have a gift.