# PERCENTAGE PROBLEMS SHORTCUTS

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 :

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,

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