**Percentage Problems Shortcuts : **

In this section, we are going to see the shortcuts 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

or

Ratio between the given number and 100

or

Saying per 100

For example,

30 % = 30/100 or 30 : 100

**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 profit percentage are given.

Cost price = C.P, Profit percentage = P%

Then Selling price (S.P) = (100+P)% x C.P

**Shortcut 4 :**

Cost price and loss percentage are given.

Cost price = C.P, Loss percentage = L%

Then Selling price (S.P) = (100 - L)% x C.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 "Hint 1" and solve for C.P

**Shortcut 9 :**

Selling price and loss percentage are given.

How to find cost price ?

Use "Hint 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 = D%

Then, Discount value = (D% ) x M.P

Selling price (S.P) = (100 - D)% x 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 kg.

Cheated value = Original weight - False weight

Then shortcut to find profit percentage is,

**Shortcut 14 :**

**Shortcut 15 :**

Apart from the shortcuts given above, if you need practice problems on percentage, please click here.

After having gone through the stuff given above, we hope that the students would have understood "Shortcuts for solving percentage problems".

Apart from the stuff given above, if you want to know more about "Shortcuts for solving percentage problems", please click here

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