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

= (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.

If you would like to have practice problems on percentage,

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