ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

186 BRAHMAGUPTA AND ARITHMETIC
have been quoted by his commentator Pṛthūdaka Svāmī in
connection with one of his karaṇa-sūtra.¹

1. A horse was purchased by (nine) dealers in partner-
   ship, whose contributions were one, etc. up to nine;
   and was sold by them for five less than five hundred.
   Tell me what was each man's share of the sale proceed²
2. Four colleges (mathas), containing an equal num-
   ber of pupils, were invited to partake of a sacrificial
   feast. A fifth, a half, a third and a quarter (of the
   total number of pupils in the college) came from the
   respective colleges to the feast; and added to one, two,
   three and four, they were found to amount to eighty-
   seven; or, with those deducted, they were sixty seven.
   Find the actual number of the pupils that came from
   each college.³
3. Three (unequal) jars of liquid butter, of water and
   of honey, contained thirty-two, sixty and twenty-four
   Pala respectively; the whole was mixed together and
   the jars filled again. Tell me the quantity of butter,
   of water and of honey in each jar⁴.
4. प्रक्षेपयोगहृत्या लब्ध्वा प्रक्षेपका गुणा लाभाः ।
   ऊनाधिकोत्तरस्तुतोनया स्वफलमूनयुत ॥ BrSpSi. XII. 16.
5. एकाद्यैर्नव पर्यन्तैर्वणिग्भिर्मूलराशिभिः ।
   क्रीतो हयोऽसौ विक्रीतः पञ्चोनैः पञ्चभिः शतैः ।
   किमैकैकस्य तत्रासीद् ब्रूहि त्वं मिश्रकान् मम ॥
6. मठस्थानानि चत्वारि छात्राणां समसंख्यया ।
   भोक्तुं संमन्त्रितान्यासन् दीक्षायां किल यज्वना ॥
   पञ्चार्धत्रिचतुर्थांशास्तेभ्यो भोक्तुं समागताः ।
   एकद्वित्रिचतुर्युक्ता दृष्टाशीतिः ससप्तका ॥
   एवोत्तरैरथवा हीना सप्तषष्टिश्चतैऽशकाः ।
   मठेभ्यश्छात्रसंख्यां मे ब्रूहि ये चागता यतः
7. घृतोदक मधूनां ये त्रयः कलसकाः पलैः ।
   रदषष्टिजिनैः पूर्णा एकीभूतास्ततः पुनः ॥
   मिश्रेण पूरिता यावत् तावत् संख्यां न वेद्म्यहम् ।
   घृतोदकमधूनां तामेकैकत्र गतां वद ॥
   —: ० :—