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# Vedic Maths - Last Totaling 10

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

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
= 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
= 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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