ANTYAYOR DAŚAKE'PI

The Sutra simply means - numbers of which the last digits added up give 10.

This sutra is helpful in multiplying numbers whose last digits add up to 10(or powers of 10). The remaining digits of the numbers should be identical.

i.e. the Sutra works in multiplication of numbers for example:
25 and 25, 2 is common and 5 + 5 = 10
47 and 43, 4 is common and 7 + 3 = 10
62 and 68,
116 and 114.
and also for 425 and 475

The last example can be looked as digit 4 being common and 25 and 75 add upto 100.

Note that in each case the sum of the last digit of first number to the last digit of second number is 10. Further the portion of digits or numbers left wards to the last digits remain the same. At that instant use Ekadhikena on left hand side digits. Multiplication of the last digits gives the right hand part of the answer.
Example 1 : 57 X 53
See the end digits sum 7 + 3 = 10 ; then by the sutras Antyayor dasakepi and Ekadhikena we have the answer.
Ekadhikena to the remaining digits means, increment the remaining digits by 1 and multiply it with the same.
57 x 53 = ( 5 + 1 )x5 / 7x3 ( the '/' is just a seperator and not a division mark)&nbsp = 30 / 21
= 3021.

Example 2: 62 x 68
2 + 8 = 10, L.H.S. portion remains the same i.e.,, 6.
Ekadhikena(increment) of 6 gives 7
62 x 68 = ( 6 x 7 ) / ( 2 x 8 )
= 42 / 16
= 4216.

Use Vedic sutras to find the products

1. 125 x 125
2. 34 x 36
3. 98 x 92

It is further interesting to note that the same rule works when the sum of the last 2, last 3, last 4 - - - digits added respectively equal to 100, 1000, 10000 -- - - . The simple point to remember is to multiply each product by 10, 100, 1000, - - as the case may be . Your can observe that this is more convenient while working with the product of 3 digit numbers.
Eg. 1: 292 x 208
Here 92 + 08 = 100, L.H.S portion is same i.e. 2
292 x 208 = ( 2 x 3 ) / 92 x 8
= 60 / 736 ( for 100 raise the L.H.S. product by 0 )
= 60736.

Find the following products using ‘Antyayordasakepi’

1. 318 x 312
2. 425 x 475