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,

Please click here

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WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

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

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and Venn diagrams

Word problems on ages

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 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

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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