विनजीत वैदिक अंकगणित पुस्तक || 1 || अध्याय 12.02 || गुणा (02) अन्त्योर्शतकेऽपि विधि
Vinjeet Vedic Arithmetic Book || 1 || Chapter 12.02 || Multiplication (02) Antyorshatkeapi method
Author
लेखक

ॐ जितेन्द्र सिंह तोमर
(M.A., B. Ed., MASSCOM, DNYS )
(Specialist in Basic and Vedic Maths)
Ekadhikane Purvena Subsutra
(Antyorshatkeapi अन्त्योर्शतकेऽपि)
Multiplycation of numbers ending whose sum of unit is 100.
गुणा
निखिलांक उपप्रमेय नंबर 3
→अन्त्योर्शतकेऽपि
Multiply
Nikhilank Corollary No. 3
Antyorshatkeapi
A BC × A DE जहां पर (BC + DE = 100)
हम देखते हैं कि इनमें दोनों के 'पूर्व' अंक एक समान ही हैं अर्थात A है और अंतिम' अंकों का योग 100 है।
जिन अन्त्योर्शतकेऽपि अंकों का योग और 100 या 100 का गुणज होता है उन्हें अन्त्योर्शतकेऽपि कहते हैं।
A BC × A DE where (BC + DE = 100)
We see that both of them have the same 'first' digit i.e. A and the sum of the 'last' digits is 100.
The antyorshatkeapi which has sum of digits and 100 or multiples of 100 is called antyorshatkeapi.
A BC × A DE जहां पर Where (BC + DE = 100)
A × •A / BC × DE
अन्तोदर्शकेऽपि विधि से वर्ग
सूत्र
=(निखिलांक) × (निखिलांक का एकाधिकेन) / (अन्त्योर्शतकेऽपि)1 × (अन्त्योर्शतकेऽपि)2
Squaring by antyorshatkeapi method
Formula
=(Nikhil ank) × (ekadhikene of nikhil ank) / (antyorshatkeapi)1 × (antyorshatkeapi)2
द्ववतीय स्थिति (Second Condition)
उपसूत्र - अन्त्योर्शतकेऽपि
अंतिम अंकों का योग सौ ।
(Sum of last digits is hundred .)
Subformula: Antyorshatkeapi
The sum of the last digits is one hundred.
(Sum of last digits is hundred.)
जब किन्हीं दो संख्याओं के इकाई व दहाई-अंकों (tens-ones-place) का योग (Sum) सौ (hundred) हो तथा शेष (rest) अंक (digits) समान ( equal) हो।
जैसे -
When the sum of the ones and tens is hundred and the remaining digits are equal.
As -
191 × 109, 156 × 144, 157 × 143, 295 × 205, 389 × 311
191 × 109 (91+09=100)
196 × 104, (96+04=100)
157 × 143 (57+43=100)
295 × 205 (95+05=100)
389 × 311 (89+11=100)
651 × 649 (51+49=100)
1978 × 1922 (78+22=100)
ABC × ADE
A(•A)/BC × DE
(1) 191 × 109
= 1 × ( •1) / 91 × 09
= 1 × 2 / 0819
= 2 0819
(2) 196 × 104
= 1 × (•1) / 96 × 04
= 1 × 2 / 0384
= 2 0384
(3) 295 × 205
= 2 × ( 2 + 1) / 95 × 05
= 2 × 3 / 0475
= 6 04755
(4) 389 × 311
= 3 × ( 3 + 1) / 89 × 11
= 3 × 4 / 0979
= 12 0979
Practice Time (1)
Q.1 Find the product of 101 × 191
Q.2 Find the product of 102 × 198
Q.3 Find the product of 103 × 197
Q.4 Find the product of 104 × 196
Q.5 Find the product of 105 × 195
Q.6 Find the product of 106 × 194
Q.7 Find the product of 207 × 293
Q.8 Find the product of 208 × 292
Q.9 Find the product of 309 × 391
Q.10 Find the product of 491 × 409
Q.11 Find the product of 143 × 147
Q.12 Find the product of 154 × 156
Q.13 Find the product of 165 × 135
Q.14 Find the product of 226 × 274
Q.15 Find the product of 187 × 113
Q.16 Find the product of 398 × 302
Q.17 Find the product of 149 × 141
Q.18 Find the product of 159 × 151
Q.19 Find the product of 231 × 269
Q.20 Find the product of 172 × 128
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