Vedic Maths - Last Totaling 10

As the name says ,this sutra has endings totaling to 10 (last totaling to 10).We have seen some 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

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

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

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
=12 / 25
= 1225

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

= 29 / 75
= 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 

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