Percentage can be defined as follows,
Comparing the given number to 100
or
Ratio between the given number and 100
or
Saying per 100
For example,
30% = 30/100 or 30 : 100
Let us see some shortcuts which can be useful to solve problems on percentage.
Shortcut 1 :
How to find percentage of a number in another number?
For example,
'a' is what percent of 'b'?
Shortcut 2 :
If a number is increased/decreased to another number, how to find the increase in percentage?
For example, '80' is increased to '96'.
Difference = 96 - 80
= 16
Percentage increase = (16/80) x 100%
= 20%
Shortcut 3 :
Cost price and marked up percentage are given.
Cost price = C.P, Profit percentage = m%
Then,
Selling price (S.P) = (100 + m)% ⋅ C.P
Shortcut 4 :
List price and marked down percentage are given.
List price = L.P, Marked down percentage = m%
Then,
Selling price (S.P) = (100 - m)% ⋅ L.P
Shortcut 5 :
Profit = S.P - C.P
Loss = C.P - S.P
Shortcut 6 :
When cost price and profit are given,
Shortcut 7 :
When cost price and loss are given,
Shortcut 8 :
Selling price and profit percentage are given.
How to find cost price?
Use shortcut 1 and solve for C.P
Shortcut 9 :
Selling price and loss percentage are given.
How to find cost price?
Use shortcut 2 and solve for C.P
Shortcut 10 :
Marked Price : It is the price before discount given
Selling price = Marked price - Discount value
Shortcut 11 :
Marked price = M.P, Discount percentage = D%
Then, the discount value is
= D% ⋅ M.P
Selling price is
= (100 - D)% ⋅ M.P
Shortcut 12 :
When marked price and discount value are given,
Shortcut 13 :
Retailer using false weight :
A trader cheats his customer to make a profit by stating that he sells at cost price. But he gives his customer less than 1000 grams (false weight) for every 1 kilogram. Then
Shortcut 14 :
Two articles are sold at the same price. But, one is sold at a profit of p% and other one is sold at a loss of p%.
Then, the net result of the transaction is loss.
The loss percentage is
= (p^{2}/100)%
Shortcut 15 :
The cost price of two articles is same. But, one is sold at a profit of p% and other one is sold at a loss of p%.
Then, the net result of the transaction is no profit and no loss.
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