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,

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...