Amazing Math Tricks Posted by : Deepak Kumar

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Percentage Shortcut 1: If we increased any value by x % and then decreased by y %. Then the resulting effect in percent will be:  “+ x + y + xy /100”.

Various Examples related to this Percentage Short cuts are given below:
Example 1:  The price of goods is marks 20% more than the real price by the shopkeeper. After that the shopkeeper allowed a discount of 10%. Now What profit or loss did the shopkeeper will get?
Solution: We solve this as follow by using the percentage shortcut1 as follow:
The Loss (or) Profit he will get is = 20 – 10 + (+20) (-10)/100
                                                     = + 8% (profit).

Example 2: Side of the square is increased by 30%. Find the percentage increase in area.
Solution: Here we again use the percentage shortcut 1.
So the increased area percentage = 30 + 30 + (30) (30)/100
                                                   = 69 % (increased).

Example 3: Radius of the circle is decreased by 20%. What will be the percent change in area of the circle?
Solution: Therefore by using the percentage shortcut1:
The Percent change in area of circle is= - 20 - 20 + (-20) (-20)/100
                                                         = -36% (decreased)

Example 4: The price of a car is increased by 15% than after that again decreased by 15%. What will be the percent change?
Solution: The percent change is = + 15 - 15 + (+15)(-15)/100
                                                  = - 2.25 % (decreased)

Example 5: Length of a rectangle is increased by 40% and breadth of the rectangle is decreased by 40%. Find change in area.
Solution: By using the formula of percentage shortcut given above:
The percent change in area of rectangle is= 40 - 40 + (-40) (+40)/100
                                                              = -16 %( decreased)

Percentage Shortcut (2):  If the price of the any product is increased or decreased by “r%” then there is decrease in the consumption so as not to increase the expenditure:   “ r/100+ r *100”, (We add when there is increase and subtract when there is decrease in percentage).

Now we will take four different examples with different problems to make this percentage shortcut concept clear to you. So take a deep look into this and understand it properly.

Example 1: Suppose if the price of salt falls down by 10%. Now how much percent (%) must increase by the householder so that its consumption remain same as there is no decrease the expenditure.
Solution: By using percentage shortcut (2):
The increase in consumption= 10/100-10*100
                                                          =11.11% (Increase the Consumption)

Example 2: If the employee A’s salary is 25% more than the employee B. Then how much percent (%) the salary of B's is less than that of salary of employee A.
Solution: Again by using the Percentage Shortcut (2) we have the following:
B's salary is less than that of employee A salary =25/100+25*100
                                                 =20 %( B salary is 20% less than the salary of A)

Example 3: Now if the employee A's salary is 30% less than that of B then how much percent is B's salary is more than that of employee A.
Solution:  Employee B's salary is more than that of A= 30/100-30*100
                                      =42 %( Employee B salary is 42% is more than Employee A)

Example 4: The price of Diesel is increased by 30%. By how much Diesel a car owner must reduce his consumption in order to maintain the same budget.
Solution: Reduction in consumption of diesel: 30/100+30*100
                                                        = 300/13 %( Reduction in the consumption)
SHORTCUT (1): To find out the selling price in any item in any given question we have to use the following shortcut formula:
Selling Price (sp) = (100 + (gain/loss)) /100 * Cost Price (CP)
Now by using the above formula we can solve any math problem related to profit and loss within few second. Lest see some example related to this formula:

Example (1): A person bought a bicycle for Rs 250. For how much should he sell it so as to gain 10% profit on it?
Solution: In this problem we have to find out the selling price for which the person will get the 10% profit. So by using the Maths Shortcut (1) we have:
Selling Price (SP) = (100 + 10)/100 * 250
                       = 275 (So selling price should be this one to gain the 10% profit on it)


Example (2): A shopkeeper purchased a Book for Rs 560. For how much he should sell it so he gets 10% loss on it.
Solution: Again by using the Maths Shortcut (1). But in this we have to find out the selling price so that loss occur so we have to use subtraction as shown below in the solution.
Selling Price = (100 – 10) / 100* 560
                      = 504
Profit and Loss Shortcut(2): Let's say any 'a' articles are bought for Rs 'b' after that the articles are sold to them to 'c' for Rs 'd'.


So the profit or loss made by the vender is    ((a*b) – (b*c))
                                                                         =   ------------------- * 100
                                                                                      b * c 
Now let’s see some examples related to this Profit and Loss shortcut.

Profit and Loss Example (1): If a person buy 11 mangos for Rs.10 after that he sell only 10 for Rs 11. How much profit or loss did the person make?

Solution:
By using the shortcut (2): Profit or loss made ((11*11) – (10*10))
                                                                           =   ---------------------------  *100
                                                                                         10*10   
                                                                           = 21% (Profit)


Profit and Loss Example(2): If a man buy 9 oranges for Rs.16 and sell 11 of them for Rs 20. Find profit or loss percent.

Solution:
Profit or loss percent made   ((9*20) – (11*16))
                                              =  --------------------------  *100
                                                          11*20
                                              = 25/11 %.