Be-Fast on calculation

1. Squaring a number with lightning fast speed
Well you might have come across various tricks to find the square of a number, but I can bet you that my trick is the simplest and the fastest :)
Firstly memorize squares of numbers upto 25. I think many of you might be knowing it already, but for those who don't, please mug it. Now this trick will help you in squaring numbers upto 125 and trust me, for SSC you need this much only.
(a) For numbers close to 50
(i) Numbers less than 50
(ii) Numbers greater than 50
The process is almost same - Compute (N - 50)
Add this difference to 25
E.g. 56*56=
1. 56 - 50 = 6
2. Last two digits = 6 * 6 = 36
3. First two digits = 25 + 6 = 31
Therefore, 56 * 56 = 3136
(b) Numbers close to 100
(i) Numbers less than 100
(ii) Numbers greater than 100
The process is almost same - Compute (N - 100)
Add this difference to N
E.g. 107*107=
1. 107 - 100 = 7
2. Last two digits = 7 * 7 = 49
3. First three digits = 107 + 7 = 114
Therefore, 107 * 107 = 11449
2. Squaring a number containing only '1'. E.g. 111, 1111, 1111111, etc.
Just count the number of ones. Like in 1111, there are 4 ones. So the square of 1111 is 1234321 (go from 1 to 4 and then back). Similarly, the square of 111111 = 12345654321
3. Finding product of two numbers of the form ab and ac, such that b+c=10. E.g. product of 43 and 47 Last two digits = 3*7 = 21
First two digits = 4*(4+1) = 20
Hence 43*47 = 2021
4. Finding product of two numbers close to 100
(a) 103*109
Last two digits = 3*9 = 27
First three digits = (103 + 9) or (109 + 3) = 112
So 103*109 = 11227
(b) 92*97
Last two digits = 8*3 = 24 [100 - 92 = 8 and 100 - 97 = 3]
First two digits = (92 - 3) or (97 - 8) = 89
Hence 92*97 = 8924
Bonus Hack :
A very common question if SSC -
I will tell you a formula that no 'paramount' will tell you :P
Note : Always take the difference between numerator and denominator as positive.
Answer : 3/(4-3) * 20 = 60 minutes
Next question -
Rakesh runs at 5/4 of his usual speed and reaches the playground 5 minutes earlier. What is his usual time?
Answer : 5/(5-4) * 5 = 25 minutes
Matter by :- Prashant Raj!