Percentage Problems Shortcuts :
In this section, we are going to see the shortcut tricks which are much required to solve math problems based on percentage.
First let us understand what is percentage.
Percentage can be defined as follows,
Comparing the given number to 100
Ratio between the given number and 100
Saying per 100
30 % = 30/100 or 30 : 100
Shortcut 1 :
How to find percentage of a number in another number ?
"a" is what percent of "b" ?
Shortcut 2 :
If a number is increased/decreased to another number, how to find the increase in percentage ?
"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%
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%
Selling price (S.P) = (100 - m)% ⋅ L.P
Shortcut 5 :
Profit = S.P - C.P
Loss = C.P - S.P
Shortcut 6 :
Cost price and Profit are given.
Cost price = C.P, Profit = K
Shortcut 7 :
Cost price and Loss are given
Cost price = C.P, Loss = K
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 :
Marked price (M.P) and discount value are given.
Then shortcut to find the discount percentage is,
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, the profit percentage is
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
= (p2 / 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.
If you would like to have practice problems on percentage,
After having gone through the stuff given above, we hope that the students would have understood, how to use shortcut tricks to solve problems on percentage.
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