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Calculate Percentages on your finger tips

Posted by: Deepak Upadhyay Posted date: 22:21 / comment : 0


  • In order to calculate 1% of any number, we simply put a decimal after the second digit from right hand side.
               Ex: 1% of 544 = 5.44
  • To calculate 10% of any number, we put a decimal after the first digit from the right.
               Ex: 10% of 544 = 54.4
  • Calculating 100% of a number is the easiest. We simply write the given number as it is.
           Ex: 100% of 544 = 544
  • To Calculate 50% of a number, we half the number by dividing it by 2.
              Ex: 50% of 544/2 = 272

 

  •    Calculating 5% of a number is also not very difficult. First calculate 10% of the    number and then half the value by dividing it by 2.
              
  
             
               Ex: 5% of 544 =?
               First calculate 10% of 544
               10% of 544 = 54.4
                And then half the value
                i.e. 54.4/2 = 27.2
  • To calculate 15% of a number, we follow these steps:
Step 1: Calculate the 10% of the number.
Step 2: Calculate the 5% of the number.
Step 3: Add the values obtained in Step 1 and Step 2.
 
              Ex: 15% of 544 = ?
              Step 1: 10% of 544 = 54.4
              Step 2: 5% of 544 = 27.2
              Step 3: 54.4 + 27.2 = 81.6
 
·         To calculate 60% of a number, we follow these steps:
Step 1: Calculate the 50% of the number.
Step 2: Calculate the 10% of the number.
Step 3: Add the values obtained in Step 1 and Step 2
  
    Ex: 60% of 544 = ?
              Step 1: 50% of 544 = 272
              Step 2: 10% of 544 = 54.4
              Step 3: 272 + 54.4 = 326.4
 
·         To calculate 95% of a number, we follow these steps:
Step 1: Calculate the 5% of the number.
Step 2: Subtract the value obtained in step 1 from the number.
   
           
 
              Ex: 95% of 544 = ?
              Step 1: 5% of 544 = 27.2
              Step 2: 544 - 27.2 = 516.8
 
 
 
 

Probability Shortcuts

Posted by: Deepak Upadhyay Posted date: 00:12 / comment : 0






Squaring the numbers - Shortcuts

Posted by: Deepak Upadhyay Posted date: 00:59 / comment : 0


Squaring 11n:

If there are two digits then,
Step-1: we write the first two natural numbers (i.e., 1 and 2)
Step-2:then we write reverse

Example 112= 12  (step-1,we write the first two natural numbers)
                  = 121 (step-2,then we write reverse)

If there are three digits then we write first three natural numbers and then we write reverse.

Example 1112 = 123     (step-1,we write the first three natural numbers)
                     = 12321 (step-2,then we write reverse)

If there are four digits then we write first four natural numbers and then we write reverse.

11112= 1234 321

Squaring a number with unit digit as 5:

Let’s say the number is R5

Now, the trick is R52 = R (R+1)/25

(here, the sign '/' does not mean division, instead it means that we have to always write 25 on the right hand side of the answer)

252 = 2 (2+1)/25
      = 625

352 = 3 (3+1)/25
     = 1225

1152 = 11 (11+1)/25
       = 11*12/25
       = 13225

Squaring a number nearer to 10n:


Let’s say you have to find the value of 962

First, find how far is 96 from 100. It is 4 digits far.

Now, write it as

962 = (96+4) (96-4) + 42

= 100*92 + 16

= 9200 + 16

= 9216

If you practice this squaring trick well, the whole calculation can be done mentally, without using a pen.

Let’s take few more examples……………………

1022 = (102 + 2) (102– 2) + 22

       = 104 * 100 + 4

      = 10404

9952 = (995 + 5) (995– 5) + 52

        = 1000 * 990 +25

        = 990000 + 25

        = 990025

10082 = (1008 + 8) (1008 - 8) + 82

          = 1016 * 1000 + 64

         = 1016064

Universal rule of squaring any number:

(ab)2  = a2 / 2ab/b2

342 = 32 / 2*3*4/42

      = 9/24/16

      = 1156

More solved problems based on Ages

Posted by: Deepak Upadhyay Posted date: 00:24 / comment : 0


Ex.2 At present the age of father is 5 (Y) times that of the age of his son. After 3 (t) years, the father’s age would be 4 (x) times the age of his son. Find the present ages of the father and the son?

Solution by conventional method

 

Let the present age of son = x yrs.

then, the present age of father = 5x yrs.

After, 3 years,

4(x+3) = 5x+3

or, 4x+12=5x-3

x = 9 yrs.

So, the son's age is 9 yrs.

Father's age = 45 yrs.

 

Shortcut Method:

 

Son's age =    t(x-1) / (x-y)

 

The value of x can be identified easily as it will be given it the same sentence where you find value of t.

In the above formula the denominator must results in a positive value. If you think the value will come negative then reverse the denominator as (y-x)

I mean you have to always subtract the greater no. from the smaller no. so that the value obtained is always positive.

In the above example

t= 3 yrs.

x = 4

y= 5

Putting the values in the above equation

Son’s age = 3 (4-1) / 5-4

=9

and father’s age = 45 yrs.

 

Ex-3 Three years (t1) earlier the father was 7 times (x) as old as his son. Three years (t2) hence, the father’s age would be 4 times (z) that of his son. What is the present age of the son?

Solution by conventional method

 

Let the present age of son = x yrs.

then, the present age of father = y yrs.

3 years earlier,

7(x-3) =y-3

or, 7x-y=18 ………. (1)

After, 3 years,

4(x+3) = y+3

or, 4x+12=y+3

or, 4x-y=-9………...(2)

Solving (1) and (2) we get, x = 9 yrs. and y = 45 yrs.

 

Shortcut Method

Son’s age = [t2 (z-1) + t1 (x-1)]/ (x-z)

= [3(4-1) + 3(7-1)]/ (7-4)

= (9+18)/3

= 27/3

= 9

 

Try yourself:

 

1.   The age of a man is 4 times that of his son. Five years ago the man was 9 times as old as his son was at that time. What is the present age of the man? (Answer- 42 yrs.)

 

2.   After 5 years the age of a father will be thrice the age of his son, whereas 5 years ago, he was 7 times as old as his son was. What are their present ages? (Son’s age=10 yrs. and Father’s age= 40 yrs.)

 

If you have any doubt/suggestion, feel free to ask in the below comment box.

Shortcuts for Age based problems

Posted by: Deepak Upadhyay Posted date: 18:49 / comment : 0 , ,


Have a look at the following questions
Ex.1 The ages of the father three years ago was 7 times the age of his son. At present the father's age is five times that of his son? what are the present ages of the father and the son?
Solution by conventional method

Let the present age of son = x yrs.
then, the present age of father = 5x yrs.
3 years ago,
7(x-3) = 5x-3
or, 7x-21=5x-3
or, 2x=18  
x = 9 yrs.
So, the son's age is 9 yrs.
Father's age = 45 yrs
Shortcut Method:

Son's age =t(x-1) / x-y
In the above example
t= 3 yrs.
X = 7
Y = 5
Putting the values in the above equation
Son’s age = 3 (7-1) / 7-5
= 18/2
=9
And father’s age = 45 yrs.


Posted by: Deepak Upadhyay Posted date: 18:56 / comment : 0

Addition of Decimals (shortcuts)

 
 
    13.6 + 7.25
= (13 + 7) + (0.6 + 0.25) [ here we first add the rounded numbers together and then
                                           we add the decimal numbers]
= 20 + 0.85
= 20.85


Posted by: Deepak Upadhyay Posted date: 13:33 / comment : 0

  1. Adding by breaking down : This is a very simple but extremely helpful trick for the bank po, bank clerk or other competitive exams with which you can add the two or more numbers mentally in quick time without using a pen.
 Example-1             
                             37 + 46


Step-1 we add the place values of  tens digits of both the numbers(highlighted in red)
                    
                            30 + 40 = 70
Step-2 Now, we add the unit digits of both the numbers separately(highlighted in blue)

                             7 + 6 = 13

Step - 3 Finally, we add the values we get at steps 1 and 2 together.

                            70 + 13 = 83

Calculation

Posted by: Deepak Upadhyay Posted date: 13:31 / comment : 0

Cubes up to 20

Posted by: Deepak Upadhyay Posted date: 12:18 / comment : 0

13
1
23
8
33
27
43
64
53
125
63
216
73
343
83
512
93
729
103
1000
113
1331
123
1728
133
2197
143
2744
153
3375
163
4096
173
4913
183
5832
193
6859
203
8000


Squares up to 30

Posted by: Deepak Upadhyay Posted date: 11:41 / comment : 0

Squares up to 30 

 
12
1
22
4
32
9
42
16
52
25
62
36
72
49
82
64
92
81
102
100
112
121
122
144
132
169
142
196
152
225
162
256
172
289
182
324
192
361
202
400
212
441
222
484
232
529
242
576
252
625
262
676
272
729
282
784
292
841
302
900

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