As the name says ,this sutra has endings totaling to 10 (

85

25 x 65

15 x 75

35 x 85

This can be extended further :

27 x 23

becomes

= 2(2+1) / (7x3)

= 6 / 21

= 621

86 x 84

= 8 (8+1) / (6x4)

= 8x9 / 24

= 72 / 24

= 7224

Similarly for any last two or three digit number totaling 100,1000 etc,we can apply the same sutra ,

884 x 816

= 8 (84) x 8 (16)

= 8x9 / (84x16)

= 72/1344 ..add zero to left hand side and carry over 1

= 720/1344 carry over the nearest digit ..i.e;'1'

= 721344

*last totaling to 10*).We have seen some examples in our first sutra " by one more than the previous too ".

__1.__

**Squaring Numbers Ending In 5**85

^{2}

First two digits = the ten’s digit times one more than the ten’s digit.

Here ,the last two digits are always 25

8(8+1) / 25

= 72/ 25

= 7525

= 7525

__2.__

**Consecutive Decades 65 x 75**
First two digits = the small ten’s digit times one more than the large ten’s digit.

Here, the last two digits are always 75

6(7+1) / 75

= 48 / 75

= 4875

= 4875

__3.__

**Ten’s Digits Both Even and ending in 5 :**25 x 65

First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits.

Last two digits are always 25

2(6) + ½ (2+6) / 25

= (12 + 4) / 25

= 16 /25

= 1625

= 16 /25

= 1625

__4.__

**Ten’s Digits Both Odd and Ending in 5 :**15 x 75

First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits.

Last two digits are always 25

1(7) + ½ (1+7) / 25

= (7+4) / 25

= 11 / 25

= 1125

= 11 / 25

= 1125

__5.__

**Ten’s Digits Odd&Even and Ending in 5:**35 x 85

First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Always drop the remainder

Last two digits are always 75

3(8) + ½ (3+8) / 75

= (24+5) / 75

= (24+5) / 75

= 29 / 75

= 2975

= 2975

This can be extended further :

__1.__**For same digits appearing on L.H.S and digits totaling 10 on R.H.S**27 x 23

becomes

= 2(2+1) / (7x3)

= 6 / 21

= 621

86 x 84

= 8 (8+1) / (6x4)

= 8x9 / 24

= 72 / 24

= 7224

Similarly for any last two or three digit number totaling 100,1000 etc,we can apply the same sutra ,

884 x 816

= 8 (84) x 8 (16)

= 8x9 / (84x16)

= 72/1344 ..add zero to left hand side and carry over 1

= 720/1344 carry over the nearest digit ..i.e;'1'

= 721344

Vedic Maths is a beautiful system if practiced properly.

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