पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

ANSWERS TO EXAMPLES 93

1. 55 ; 210 ; 465 ; 820 ; 1275 ; 1830 ; 2485 ; 3240 ; 4095 ;
2. 10 ; 20 ; 30 ; 40 ; 50 ; 60 ; 70 ; 80 ; 90 ; 100.
3. 4995 ; 4840 ; 4585 ; 4230 ; 3775 ; 3220 ; 2565 ; 1810 ; 955 ; 0.
4. 27216 ; 33152 ; 483900 . 4. 1, 4, 9, 16, 25, 36, 49, 64, 81, 625, 1296,
   3969, 186624, and 60871204. 5. 1 ; 8 ; 27 ; 64 ; 125 ; 216 ; 343 ; 512 ;
   729 ; 3375 ; 16777216 ; and 8365427. 6. 1 1/12 ; 11 1/4 . 7. 1 7/8 ; 3/8 ; 3/4 .
5. 1/4 ; 1/6 . 9. 13 1/2 . 10. 3 3/4 ; 150 2/5 . 11. 2 1/2 ; 17 5/14 . 12. 6 1/4 ;
   232 9/16 ; 1/4 ; 1/9 . 13. 421 7/8 ; 5132 61/64 ; 5/64 ; 2/7 . 14. 1 9/20 ; 5 1621/25200 .
6. 3103/25200 . 16. 30 . 17. 5 11/16 . 18. 15 1/12 . 19. 5 15/16 . 20. 12 11/12 .
7. 1 13/16 . 22. 5 347/6400 purâṇas. 23. 4 23/48 . 24. 10 11/12 . 25. 7 7/10
   paṇas ; or 4 purâṇas, 13 paṇas, 2 kâkiṇîs, and 16 varâṭakas. 26. 10 1/4 palas ;
   or 10 palas, 1 karṣa, 3 mâṣas, and 4 8/9 guñjâs. 27. 87 21/31 . 28. 2 droṇas,
   1 âḍhaka, and 2 177/256 prasthas. 29. 3 158/159 rûpas. 30. 8 months and 26 2/3 days.
8. 33600 years. 32. 9 34/49 days. 33. 19 4/11 days. 34. 26 2/5 necklaces.
9. 250 suvarṇas. 36. 244 suvarṇas, 5 mâṣas, and 4 7/11 guñjâs.
10. 450 blankets. 38. 122 suvarṇas, 8 mâṣas, and 4 24/49 guñjâs.
11. Interest = 36. 40. 20 135/136 . 41. 2362 1/2 . 42. 1 111/832 . 43. 38 1/4 paṇas ;
    or 2 purâṇas, 6 paṇas, and 1 kâkiṇî. 44. 60 . 45. 33 3/4 . 46. 49 7/8 .
12. 3 droṇas, 0 âḍhaka, 3 prasthas, and 1 5/7 kuḍavas. 48. 2 palas of long
    pepper. 49. 25 wood-apples. 50. 64. 51. 200. 52. Capital = 60 ;
    Interest = 36. 53. Capital = 33 1/3 ; Interest = 3. 54. Capital = 500 ;
    Interest = 300 ; share of surety = 60 ; share of calculator = 30 ; and share
    of scribe = 15. 55-56. The debtor is relieved of his debt in 2 months
    and 21 1371/1789 days. In this time the rich man gets 109 1371/1789 rûpas in all, the
    profit being 9 1371/1789 rûpas. 57-58. Principal = 1000 ; time = 8 months
    and 3 days ; and rate per cent. per month = 4. 59. Principal = 100 ;
    time = 8 months and 17 days ; and rate per cent. per month = 4 1/2 .
    60(i). 20 months. 60(ii). 7 months, 4 days, 17 ghaṭikâs, and 8 4/7 caṣakas.
13. 11 5/31 varṇas. 62. 9 15/55 varṇas. 63. 13 11/17 varṇas. 64. 16 mâṣas.
14. 11 3/4 varṇas. 66. 5 mâṣas.
    67-68. varṇa gold of varṇa 16 gold of varṇa 10
    16 2 mâṣas 0 mâṣas
    15 3/4 23/12 ,, 1/12 ,,
    15 1/2 22/12 ,, 2/12 ,,
    15 1/4 21/12 ,, 3/12 ,,
    15 20/12 ,, 4/12 ,,
    Indological Truths

94 ANSWERS
14¾ 19/12 ,, 5/12 ,,
14½ 18/12 ,, 6/12 ,,
14¼ 17/12 ,, 7/12 ,,
14 16/12 ,, 8/12 ,,
13¾ 15/12 ,, 9/12 ,,
13½ 14/12 ,, 10/12 ,,
13¼ 13/12 ,, 11/12 ,,
13 12/12 ,, 12/12 ,,
12¾ 11/12 ,, 13/12 ,,
12½ 10/12 ,, 14/12 ,,
12¼ 9/12 ,, 15/12 ,,
12 8/12 ,, 16/12 ,,
11¾ 7/12 ,, 17/12 ,,
11½ 6/12 ,, 18/12 ,,
11¼ 5/12 ,, 19/12 ,,
11 4/12 ,, 20/12 ,,
10¾ 3/12 ,, 21/12 ,,
10½ 2/12 ,, 22/12 ,,
10¼ 1/12 ,, 23/12 ,,
10 0 2 ,,
69. One is of weight 2 māṣas and varṇa 12 ; the other is of weight 3 māṣas
and varṇa 8. 70. One is of weight 5 māṣas and varṇa 14 ; the other is of
weight 7 māṣas and varṇa 10. 71. 30 prasthas ; 45 prasthas ; 75 prasthas ;
and 60 prasthas respectively. 72. 900 prasthas, 600 prasthas, and 200 prasthas
respectively. 73-74. 49/32 kuḍavas of mudga (seeds of phaseolus mungo) and
49/64 kuḍavas of rice, the respective prices being 63/32 paṇas and 49/32
paṇas. 75. 14/37 palas of asafoetida, 14/37 palas of long pepper, and 14/37
palas of dry ginger, the respective prices being 28/37 paṇa, 7/37 paṇa, and
2/37 paṇa.
76. There will be infinite solutions. The commentator obtains two
solutions in the first case, viz.,
rate of purchase : 17 artieles for 1 } , 20 articles for 1 } ,
rate of sale : 6 artieles for 1 } 7 articles for 1 }
and one solution in the second case, viz.,
rate of purchase : 240 articles for 1,
rate of sale : 7 articles for 1.
77. One solution as given by the commentator is :
rate of purchase : 40 articles for 1,
rate of sale : 22 articles for 1.

ANSWERS 95
78-79. The following are the 16 valid integral solutions :
(1) (2) (3) (4)
Number Price Number Price Number Price Number Price
Pigeons 15 9 | 55 33 5 3 | 30 18
Cranes 28 20 | 21 15 56 40 | 21 15
Swans 45 35 | 9 7 27 21 | 36 28
Peacocks 12 36 | 15 45 12 36 | 13 39
(5) (6) (7) (8)
Number Price Number Price Number Price Number Price
Pigeons 10 6 20 12 15 9 | 35 21
Cranes 42 30 14 10 63 45 | 42 30
Swans 36 28 54 42 9 7 | 9 7
Peacocks 12 36 12 36 13 39 | 14 42
(9) (10) (11) (12)
Number Price Number Price Number Price Number Price
Pigeons 20 12 | 40 24 60 36 | 25 15
Cranes 49 35 | 28 20 7 5 | 35 25
Swans 18 14 | 18 14 18 14 | 27 21
Peacocks 13 39 | 14 42 15 45 | 13 39
(13) (14) (15) (16)
Number Price Number Price Number Price Number Price
Pigeons 45 27 35 21 5 3 | 10 6
Cranes 14 10 7 5 21 15 | 7 5
Swans 27 21 45 35 63 49 | 72 56
Peacocks 14 42 | 13 39 | 11 33 | 11 33
Of these sixteen solutions, the first four have been given by the com-
mentator.
80. The commentator gives the following solutions :
(1) (2) (3) (4) (5)
Fruits Prices Fruits Prices Fruits Prices Fruits Prices Fruits Prices
Pomegranates 16 32 | 17 34 | 19 38 | 18 36 | 15 30 |
Mangoes 60 36 | 45 27 | 15 9 | 30 18 | 75 45 |
Wood-apples 24 12 | 38 19 | 66 33 | 52 26 | 10 5 |
81-82. After 8 days, 21 1/11 ghaṭikās. 83. The meeting takes place
after 20 days when the travellers are at a distance of 40 yojanas from the
starting place. 84-85. 2 paṇas and 3 kākiṇīs. 86-87. 6, 14, 26, and
50 respectively. 88. The two persons stopping away after going
over 1 krośa receive 6 2/3 ; the three persons stopping away after going over
2 krośas get 22 1/2 ; and the five persons who go over 3 krośas receive 70 5/6 .
89-90. 12, 27, 47, 77, and 137 respectively. 91. 1 1/7 of a day.

96 ANSWERS
92. 4 jack-fruits. 93-94. 2 krośas and 3 krośas respectively.
95. 63. 96. 12 cubits. 97. 360. 98. 20 cows. 99. 36.
100. 9. 101. 25. 102. 24/5. 103(i). 40 ; 8/3. 103(ii). 0.
104-105. 2 paṇas and 2¾ kākiṇīs. 106. 29½. 107. 6¾. 108.
206158430208. 109. 93. 110. 252 paṇas. 111. 15 days. 112.
If the first traveller travel with speed 1 and acceleration 6 and meet
the second traveller for the first time after 10 days, then the second
meeting of the two travellers will occur 8 days after the first meeting.
113. The first man wins, the amount won being 48360. 114. The
second man wins, the amount won being 101⁷. 115. The second
man wins, the amount won being 25. 116(i). 165. 116(ii). 55.
117. 3025 ; 220. 118. 588. 119 699. 120. 986. 121.
2528. 122. 2¼ square cubits. 123. 15½ square cubits. 124.
5¼ square cubits. 125. 31 ⁴¹/₁₄₄ square cubits. 126. 12 square
cubits. 127. 16 square cubits. 128. 768 square cubits.
129-130. 46 ¹²⁷/₁₄₅₆ square cubits. 131. 3 square cubits ; 30 square
cubits. 132. 12 square cubits. 133. 35 square cubits.

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