matha namo namaha


ANTYAYOR DAŚAKE′PI
The Sutra signifies numbers of which the last digits added up give 10. i.e. the Sutra works in multiplication of numbers for example: 25 and 25, 47 and 43, 62 and 68, 116 and 114. 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 :  47 X 43
See the end digits sum 7 + 3 = 10 ; then by the sutras antyayor dasakepi and ekadhikena we have the answer.

            47 x 43 = ( 4 + 1 ) x 4 / 7 x 3
                        = 20 / 21
                        = 2021.
Example 2:  62 x 68

          2 + 8 = 10,  L.H.S. portion remains the same i.e.,, 6.

          Ekadhikena of 6 gives 7

             62 x 68 = ( 6 x 7 ) / ( 2 x 8 )
                         =  42 / 16
                         = 4216.
Example 3:   127 x 123

        As antyayor dasakepi works, we apply ekadhikena

            127 x 123 = 12 x 13 / 7 x 3
                           = 156 / 21
                           = 15621.
Example 4:  65 x 65

        We have already worked on this type. As the present sutra is applicable.

            We have 65 x 65 = 6 x 7 / 5 x 5
                                     = 4225.
Example 5:  3952

            3952 = 395 x 395
                    = 39 x 40 / 5 x 5
                    = 1560 / 25
                    = 156025.
Use Vedic sutras to find the products

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

        4.  401 x 409            5.  693 x 697        6. 1404 x 1406
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.
Eg. 2:   848 X 852

        Here 48 + 52 = 100,  L.H.S portion is 8 and its ‘ekhadhikena’ is 9.

        Now R.H.S product 48 X 52 can be obtained by ‘anurupyena’ mentally.
                           _
                    48    2
                    52    2
                   _______
                            _
               2)  50    4     =   24 / ( 100 – 4 )
                    ¯¯
                    25               = 96

                                 = 2496

        and write 848 x 852 = 8 x 9 / 48 x 52

                             720 = 2496

                                          = 722496.

     [Since L.H.S product is to be multiplied by 10 and 2 to be carried over as the base is 100].
Eg. 3:   693 x 607

            693 x 607 = 6 x 7 / 93 x 7
                           = 420 / 651
                           = 420651.
Find the following products using ‘antyayordasakepi’

            1.  318 x 312             2.  425 x 475         3.  796 x 744

            4.  902 x 998             5.  397 x 393         6.  551 x 549

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