Shortcut-1

To multiply two numbers having difference of “10” and at last there is “5” 



Let’s take an example:

65*75

Answer will be in 2 parts:

On right hand side there will be “75”

() (75)

Now, let’s find left hand side:

In numbers “65” and “75”:

Left hand sides are ‘6’ and ‘7’

Take square of bigger number: ‘7’

Square of (7) = 49

Now, subtract “1” from “49”.

We will get answer:

4875

Hence

“To multiply two numbers having difference of 10 and at last there is 5”

First write on right hand side “75”

For Left hand Side:

Check left hand side of both the numbers.

Take bigger left hand side number

and square it

Subtract “1” from it to get left hand side of the answer.

Let’s take more examples:

135 * 145

Step – 1:

Write “75” on right hand side.

Step – 2:

 In numbers “135” and “145”

Left hand sides are “13” and “14”

Bigger one is: “14”

 Square of “14” is “196”

Subtract ‘1’ from “196”

We will get:

“195”

Hence:

Answer is:

135*145 = 19575

105*115 =?

Step – 1:

Write “75” on right hand side.

Step-2:

Left hand sides of “105” and “115” are:

“10” and “11”:

Bigger number is “11”:

Square of “11” is = 121

Subtract “1” from “121”

WE will get “120” as left hand side.

Hence:

Answer is:

105 * 115 = 12075