DI concept

Percentage concepts
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When a number becomes double, we say that it increased by 100%.
Also if it becomes thrice,the number increased by 200%.
ie the percentage increase ,if number got multiplied by ‘n’ times is
(n-1)*100.
If the number increases 14 times,the percentage increase is (14-1)*100=1300%

Similarly,if we say that a number got percentage increase of 1200,we mean that it became,{(1200/100) +1} ie 13 times its original value.

Also finding the squares of numbers, quickly is another important need for scoring high marks in DI section.

Fast way of finding Squares of numbers.
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For finding squares of all numbers,we have a rather easy way.

Eg 1.Find the square of 32.

(32-2)*(32+2)+2*2= 30*34+4=1020+4=1024.

The advantage of this method is that we are converting the squaring procedure to a single digit multiplication plus addition. This is quite easy compared to the usual 2-digit multiplication.
In the example given above,the 32*32 multiplication is changed to a simple single digit multiplication of 34*3. and addition.

Eg. 2. Find the square of 26.

(26-6)*(26+6)+6*6=20*32+36=640+36=676
or this can be done in one more way,
(26+4)(26-4)+4*4=30*22+16=660+16=676.

Both ways are easier than the original multiplication of 26*26.

We can do any square using this method; however we need to improve our speed in single digit multiplication.

Faster way of finding Square-roots of numbers
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Finding approximate roots of numbers can also be useful in DI sections.
We have an easy method for that too.

Eg1. Suppose we need to find the root of 30.

The largest number with its square within 30 is 5(5*5=25).
Now 30/5 is 6.
So square root of 30 is (5+6)/2 = 5.5

If you take the square root of 30,it will come to 5.477. Approximately 5.5.

Eg2. Find the root of 40.

The largest number with its square within 40 is 6(6*6=36).
Now 40/6 is 6.667
So square root of 40 is (6+6.667)/2 = 6.333.
If you take the square root of 40,it will come to 6.324. Approximately 6.333...