# 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 :

When cost price and profit are given,

Shortcut 7 :

When cost price and loss are given,

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 :

When marked price and discount value are given,

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

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.

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